1 Foundations 2 Solving Linear Equations 3 Graphs And Functions 4 Systems Of Linear Equations 5 Polynomials And Polynomial Functions 6 Factoring 7 Rational Expressions And Functions 8 Roots And Radicals 9 Quadratic Equations And Functions 10 Exponential And Logarithmic Functions 11 Conics 12 Sequences, Series And Binomial Theorem Chapter6: Factoring
6.1 Greatest Common Factor And Factor By Grouping 6.2 Factor Trinomials 6.3 Factor Special Products 6.4 General Strategy For Factoring Polynomials 6.5 Polynomial Equations Chapter Questions Section: Chapter Questions
Problem 327RE: In the following exercises, solve. 327. The area of a bulletin board is 55 square feet. The length... Problem 328RE: In the following exercises, solve. 328. A rectangular carport has area 150 square feet. The height... Problem 329RE: In the following exercises, solve. 329. A pennant is shaped like a right triangle, with hypotenuse... Problem 330RE: In the following exercises, solve. 330. A stained glass window is shaped like a right triangle. The... Problem 331RE: In the following exercises, solve. 331. A reflecting pool is shaped like a right triangle, with one... Problem 332RE: In the following exercises, solve. 332. A goat enclosure is in the shape of a right triangle. One... Problem 333RE: In the following exercises, solve. 333. Juli is going to launch a model rocket in her back yard.... Problem 334RE: In the following exercises, solve. 334. Gianna is going to throw a ball from the top floor of her... Problem 335RE: Explain how you solve a quadratic equation. How many answers do you expect to get for a quadratic... Problem 336RE: Give an example of a quadratic equation that has a GCF and none of the solutions to the equation is... Problem 337RE: In the following exercises, find the greatest common factor. 337. 12a2b3,15ab2 Problem 338RE: In the following exercises, find the greatest common factor. 338. 12m2n3,42m5n3 Problem 339RE: In the following exercises, find the greatest common factor. 339. 15y3,21y2,30y Problem 340RE: In the following exercises, find the greatest common factor. 340. 45x3y2,15x4y,10x5y3 Problem 341RE: In the following exercises, factor the greatest common factor from each polynomial. 341. 35y+84 Problem 342RE: In the following exercises, factor the greatest common factor from each polynomial. 342. 6y2+12y6 Problem 343RE: In the following exercises, factor the greatest common factor from each polynomial. 343. 18x315x Problem 344RE: In the following exercises, factor the greatest common factor from each polynomial. 344. 15m4+6m2n Problem 345RE: In the following exercises, factor the greatest common factor from each polynomial. 345. 4x312x2+16x Problem 346RE: In the following exercises, factor the greatest common factor from each polynomial. 346. 3x+24 Problem 347RE: In the following exercises, factor the greatest common factor from each polynomial. 347. 3x3+27x212x Problem 348RE: In the following exercises, factor the greatest common factor from each polynomial. 348.... Problem 349RE: In the following exercises, factor by grouping. 349. axay+bxby Problem 350RE: In the following exercises, factor by grouping. 350. x2yxy2+2x2y Problem 351RE: In the following exercises, factor by grouping. 351. x2+7x3x21 Problem 352RE: In the following exercises, factor by grouping. 352. 4x216x+3x12 Problem 353RE: In the following exercises, factor by grouping. 353. m3+m2+m+1 Problem 354RE: In the following exercises, factor by grouping. 354. 5x5yy+x Problem 355RE: In the following exercises, factor each trinomial of the formx2+bx+c. 355. a2+14a+33 Problem 356RE: In the following exercises, factor each trinomial of the form x2+bx+c. 356. k216k+60 Problem 357RE: In the following exercises, factor each trinomial of the form x2+bx+c. 357. m2+3m54 Problem 358RE: In the following exercises, factor each trinomial of the formx2+bx+c. 358. x23x10 Problem 359RE: In the following examples, factor each trinomial of the form x2+bxy+cy2. 359. x2+12xy+35y2 Problem 360RE: In the following examples, factor each trinomial of the formx2+bxy+cy2. 360. r2+3rs28s2 Problem 361RE: In the following examples, factor each trinomial of the form x2+bxy+cy2. 361. a2+4ab21b2 Problem 362RE: In the following examples, factor each trinomial of the form x2+bxy+cy2. 362. p25pq36q2 Problem 363RE: In the following examples, factor each trinomial of the form x2+bxy+cy2. 363. m25mn+30n2 Problem 364RE: In the following exercises, factor completely using trial and error. 364. x3+5x224x Problem 365RE: In the following exercises, factor completely using trial and error. 365. 3y321y2+30y Problem 366RE: In the following exercises, factor completely using trial and error. 366. 5x4+10x375x2 Problem 367RE: In the following exercises, factor completely using trial and error. 367. 5y2+14y+9 Problem 368RE: In the following exercises, factor completely using trial and error. 368. 8x2+25x+3 Problem 369RE: In the following exercises, factor completely using trial and error. 369. 10y253y11 Problem 370RE: In the following exercises, factor completely using trial and error. 370. 6p219pq+10q2 Problem 371RE: In the following exercises, factor completely using trial and error. 371. 81a2+153a+18 Problem 372RE: In the following exercises, factor. 372. 2x2+9x+4 Problem 373RE: In the following exercises, factor. 373. 18a29a+1 Problem 374RE: In the following exercises, factor. 374. 15p2+2p8 Problem 375RE: In the following exercises, factor. 375. 15x2+6x2 Problem 376RE: In the following exercises, factor. 376. 8a2+32a+24 Problem 377RE: In the following exercises, factor. 377. 3x2+3x36 Problem 378RE: In the following exercises, factor. 378. 48y2+12y36 Problem 379RE: In the following exercises, factor. 379. 18a257a21 Problem 380RE: In the following exercises, factor. 380. 3n412n396n2 Problem 381RE: In the following exercises, factor using substitution. 381. x413x230 Problem 382RE: In the following exercises, factor using substitution. 382. (x3)25(x3)36 Problem 383RE: In the following exercises, factor completely using the perfect square trinomials pattern. 383.... Problem 384RE: In the following exercises, factor completely using the perfect square trinomials pattern. 384.... Problem 385RE: In the following exercises, factor completely using the perfect square trinomials pattern. 385.... Problem 386RE: In the following exercises, factor completely using the perfect square trinomials pattern. 386.... Problem 387RE: In the following exercises, factor completely using the perfect square trinomials pattern. 387.... Problem 388RE: In the following exercises, factor completely using the difference of squares pattern, if possible.... Problem 389RE: In the following exercises, factor completely using the difference of squares pattern, if possible.... Problem 390RE: In the following exercises, factor completely using the difference of squares pattern, if possible.... Problem 391RE: In the following exercises, factor completely using the difference of squares pattern, if possible.... Problem 392RE: In the following exercises, factor completely using the difference of squares pattern, if possible.... Problem 393RE: In the following exercises, factor completely using the difference of squares pattern, if possible.... Problem 394RE: In the following exercises, factor completely using the difference of squares pattern, if possible.... Problem 395RE: In the following exercises, factor completely using the difference of squares pattern, if possible.... Problem 396RE: In the following exercises, factor completely using the difference of squares pattern, if possible.... Problem 397RE: In the following exercises, factor completely using the difference of squares pattern, if possible.... Problem 398RE: In the following exercises, factor completely using the difference of squares pattern, if possible.... Problem 399RE: In the following exercises, factor completely using the difference of squares pattern, if possible.... Problem 400RE: In the following exercises, factor completely using the difference of squares pattern, if possible.... Problem 401RE: In the following exercises, factor completely using the sums and differences of cubes pattern, if... Problem 402RE: In the following exercises, factor completely using the sums and differences of cubes pattern, if... Problem 403RE: In the following exercises, factor completely using the sums and differences of cubes pattern, if... Problem 404RE: In the following exercises, factor completely using the sums and differences of cubes pattern, if... Problem 405RE: In the following exercises, factor completely. 405. 24x3+44x2 Problem 406RE: In the following exercises, factor completely. 406. 24a49a3 Problem 407RE: In the following exercises, factor completely. 407. 16n256mn+49m2 Problem 408RE: In the following exercises, factor completely. 408. 6a225a9 Problem 409RE: In the following exercises, factor completely. 409. 5u445u2 Problem 410RE: In the following exercises, factor completely. 410. n481 Problem 411RE: In the following exercises, factor completely. 411. 64j2+225 Problem 412RE: In the following exercises, factor completely. 412. 5x2+5x60 Problem 413RE: In the following exercises, factor completely. 413. b364 Problem 414RE: In the following exercises, factor completely. 414. m3+125 Problem 415RE: In the following exercises, factor completely. 415. 2b22bc+5cb5c2 Problem 416RE: In the following exercises, factor completely. 416. 48x5y2243xy2 Problem 417RE: In the following exercises, factor completely. 417. 5q215q90 Problem 418RE: In the following exercises, factor completely. 418. 4u5v+4u2v3 Problem 419RE: In the following exercises, factor complete 419. 10m46250 Problem 420RE: In the following exercises, factor completely. 420. 60x2y75xy+30y Problem 421RE: In the following exercises, factor completely. 421. 16x224xy+9y264 Problem 422RE: In the following exercises, solve. 422. (a3)(a+7)=0 Problem 423RE: In the following exercises, solve. 423. (5b+1)(6b+1)=0 Problem 424RE: In the following exercises, solve. 424. 6m(12m5)=0 Problem 425RE: In the following exercises, solve. 425. (2x1)2=0 Problem 426RE: In the following exercises, solve. 426. 3m(2m5)(m+6)=0 Problem 427RE: In the following exercises, solve. 427. x2+9x+20=0 Problem 428RE: In the following exercises, solve. 428. y2y72=0 Problem 429RE: In the following exercises, solve. 429. 2p211p=40 Problem 430RE: In the following exercises, solve. 430. q3+3q2+2q=0 Problem 431RE: In the following exercises, solve. 431. 144m225=0 Problem 432RE: In the following exercises, solve. 432. 4n2=36 Problem 433RE: In the following exercises, solve. 433. (x+6)(x3)=8 Problem 434RE: In the following exercises, solve. 434. (3x2)(x+4)=12x Problem 435RE: In the following exercises, solve. 435. 16p3=24p2+9p Problem 436RE: In the following exercises, solve. 436. 2y3+2y2=12y Problem 437RE: In the following exercises, solve. 437. For the function, f(x)=x2+11x+20 , (a) find when f(x)=8 (b)... Problem 438RE: In the following exercises, solve. 438. For the function, f(x)=9x218x+5 , (a) find when f(x)=3 (b)... Problem 439RE: In each function, find: (a) the zeros of the function (b) the x-intercepts of the graph of the... Problem 440RE: In each function, find: (a) the zeros of the function (b) the x-intercepts of the graph of the... Problem 441RE: In the following exercises, solve. 441. The product of two consecutive numbers is 399. Find the... Problem 442RE: In the following exercises, solve. 442. The area of a rectangular shaped patio 432 square feet. The... Problem 443RE: In the following exercises, solve. 443. A ladder leans against the wall of a building. The length of... Problem 444RE: In the following exercises, solve. 444. Shruti is going to throw a ball from the top of a cliff.... Problem 445PT: In the following exercises, factor completely. 445. 80a2+120a3 Problem 446PT: In the following exercises, factor completely. 446. 5m(m1)+3(m1) Problem 447PT: In the following exercises, factor completely. 447. x2+13x+36 Problem 448PT: In the following exercises, factor completely. 448. p2+pq12q2 Problem 449PT: In the following exercises, factor completely. 449. xy8y+7x56 Problem 450PT: In the following exercises, factor completely. 450. 40r2+810 Problem 451PT: In the following exercises, factor completely. 451. 9s212s+4 Problem 452PT: In the following exercises, factor completely. 452. 6x211x10 Problem 453PT: In the following exercises, factor completely. 453. 3x275y2 Problem 454PT: In the following exercises, factor completely. 454. 6u2+3u18 Problem 455PT: In the following exercises, factor completely. 455. x3+125 Problem 456PT: In the following exercises, factor completely. 456. 32x5y2162xy2 Problem 457PT: In the following exercises, factor completely. 457. 6x419x2+15 Problem 458PT: In the following exercises, factor completely. 458. 3x336x2+108x Problem 459PT: In the following exercises, solve 459. 5a2+26a=24 Problem 460PT: In the following exercises, solve 460. The product of two consecutive integers is 156. Find the... Problem 461PT: In the following exercises, solve 461. The area of a rectangular place mat is 168 square inches. Its... Problem 462PT: In the following exercises, solve 462. Jing is going to throw a ball from the balcony of her condo.... Problem 463PT: In the following exercises, solve 463. For the function, f(x)=x27x+5 , (a) find when f(x)=7 (b) Use... Problem 464PT: In the following exercises, solve 464. For the function f(x)=25x281 , find: (a) the zeros of the... Problem 335RE: Explain how you solve a quadratic equation. How many answers do you expect to get for a quadratic...
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Explain the steps in solving quadratics using the Factoring method, quadratic formula , and completing the square method. Give an example and explain when you would use this method for all 3 methods.
Formula Formula A polynomial with degree 2 is called a quadratic polynomial. A quadratic equation can be simplified to the standard form: ax² + bx + c = 0 Where, a ≠ 0. A, b, c are coefficients. c is also called "constant". 'x' is the unknown quantity
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