5. Multiply the polynomials (x + 3)(2x – 4). What is the product in the form ax? + bæ + c? Enter your answers in the boxes.

Q: 2. Decide if the following polynomials are reducible in Q[x]. (a) 2x3 – 3x + 3; (b) 4x3 — 5х + 2.

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Q: 2. Use syntr dhe hirst polynomial by the second. а. х2+x -3; х-1 b. 4x- 3x2+ 3x - 2; x-1 c. x'+x°…

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Q: In Z,[x] The quotient when 5x* + 3x² + 1 is divided by 3x² + 2x + 1 is 4x² + 3x + 6. a) True b)…

A: We decide whether given statement is true or false

Q: Show that x² − 4 is a factor of x⁴ − 5x³ + 2x² + 20x − 24

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Q: 12. When the polynomial 2a3 – 11x - 5 is divided by æ – 5, the quotient is of the form ax? +bx +c.…

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Q: Express the polynomial a+ 3 +a2 + 2r as a product of its irreducible factors in Z,lr).

A:

Q: 29. Select the quadratic polynomial with roots -1 and 4. 22 + 3x – 4 O a3 – 2a? – 7æ – 4 O 4x2 + 8x…

A: It is given that the equation is in quadratic And the two roots of the equations are -1 , 4    This…

Q: 1. Show whether the given polynomials 1+4x + x², 2+ 5x + 3x2, 3x 5x, and 3+ 15x - 8x spans p,.…

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Q: 1. The degree of the polynomial –8r* + 3r – 8r + 16 – is A. -8. B. -1. C. 4. D. 5.

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Q: Factor the Polynomial O prime O ((2/3)c + (1/4)h^2)((2/3)c - (1/4)h^2) O ((2/3)c + (1/4)h)((2/3)c -…

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Q: Which of the following polynomials has a remainder of 1 when divided by x + 2, x + 3 and x + 5? x³ +…

A: We have to find the polynomial

Q: Do the polynomials x? + 2,2x2 – x + 1,x + 2, and x² + x + 4 span P2?

A: Let u1 = x2+2, u2 = 2x2-x+1, u3 = x+2, and u4 = x2+x+4. Notice that u1 + u3 = u4. So, u1, u2, u3,…

Q: 14. Form a quadratic polynomial whose one zero is 8and product of the zeros is -56 15. If the zeros…

A: We have to find out quadratic polynomial

Q: 3) Show that (a + b +c)² = a² + b² + c² + 2ab + 2ac + 2bc is a polynomial identity.

A: To show: a+b+c2=a2+b2+c2+2ab+2ac+2bc

Q: Which of the following polynomials is a difference of​ squares? A.49x^2+64 B.7x^2-8…

A:

Q: Verify the factorization using the FOIL method. (x + 3y)(x – 7y) = x? – 7xy + 3xy – 21y² = x² – 4xy…

A: The given expression is: x+3yx-7y=x2-7xy+3xy-21y2⇒x+3yx-7y=x2-4xy-21y2    -1 Thus, we have:…

Q: 10. Use the appropriate method to solve the following polynomials. a. y = x* + 35x² – 36 - b. y =…

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Q: S. Which polynomials gives a quotlent of (3x + 2x+ 4) and a remalinder of 19 when divided by (2x-3)7…

A:

Q: How do i find the ral seros of  a given polynomial and their corresponding multiplicities?…

A: We have to find the zeroes and their multiplicities.

Q: Completly factorize x5 + 4x4 + 7x³ + 8x² + 4x + 2 in Q[x]. Justify that the found factors are…

A:

Q: Q3: Factorize f (x) = 2x* + x³ + 2x + 4 € Z5[x] as a polynomials product to irreducible over Z5?

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Q: Based on the Fundamental Theorem of Algebra, how many zeros does the polynomial z - 3z-5z +15r? -…

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Q: 9. Find the quotient and the remainder of x³ + 2x² – 1 divided by 3x2 +1 in Z7[x].

A: Note that for Z_7  Any number is equal to the remainder when it is divided by 7.

Q: (a) What is the degree of Q(7, V3) over Q ? Justify your answer. Is the polynomial X - 5 € QIX)…

A: Degree of extension- Let E be an extension field of a field F i.e. F is a subfield of E, also E is a…

Q: Which of the following polynomials will fill in the blank to make the equation true? 2 (3x - 7x + 2)…

A: The given polynomials,3x2-7x+2+_______=2x2-10x+3

Q: 35. Consider the polynomial xy + 27xyt + x²y+ 3xy². a) One factor of the polynomial x + 27y is x +…

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Q: Show that factorial polynomial represent the function: -1+2r – 3r2 + 42 is -1+ (2 – 3h + 4h²)æ(-1) +…

A: Given function, -1+2x-3x2+4x3 To show that the factorial polynomial representation of above function…

Q: (b) Find the nested form Q(x) of the polynomial /(x) = x³ + 2x2-5x + 3 and hence evaluate Q(2.6)…

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Q: Determine the number of zeros in the right half-plane (Re z > 0) of the polynomial p(2) = 23 + 22 +…

A: "Since you have asked multiple questions we will solve the first question. For the remaining kindly…

Q: 4. When the polynomial P(x) is divided by (x-2)2 the remainder is 3x - 3. What is the remainder when…

A:

Q: 5.26 st factor out th 2x + 2x-24 ect the correc A. 2x +2x

A: In mathematics, the greatest common divisor (GCD) of two or more integers, which are not all zero,…

Q: What is the sum of the polynomials? (8x² - 9y² -4x] + (x²_3y² - 7x) 2-3y2-7x 8x -9y2 -4x +

A:

Q: 2. Simplify the following polynomials: a) (x²-3x² + 5x-9) + (4x³ - 5x² - 8x +11) b) (3xyz - 4x² + 8)…

A: For solving this kind of problem we need to add same power of terms and simplify the equation.

Q: 3. What is the kvalue for the polynomial x - 7x + 17x – 15 if a factor is x – 3? A. k= -3 B. k= 3 C.…

A: We can use factorisation in order to solve the given problem.

Q: 1. Classify the following polynomial by degree and by the number of terms 3. 2 7x° + 2x + 3x + 9

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Q: (4) Find a polynomial that has 1+i and 1- i as zeros.

A: We have to find polynomial

Q: I. Use the Factor Theorem to determine whether the given binomial of the form x - c is a factor of…

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Q: Multiply the polynomials  \left(x+3\right)(2x-4)(x+3)(2x−4). What is the product in the form…

A: Here we will multiply given polynomials,

Q: Used synthetic dIVision to find the other factors o 1. (2x + x³ + 7x² – 40), (x – 2) 2. (-9x² + 2x³+…

A: Use synthetic division to solve

Q: b. Find a QR-factorisation of 1 -1 1 1 1 1 -1 0 |

A: Step:-1 Given matrix  is  110-1010111-10 Let  A= 110-1010111-10 Now, we'll apply Gram-Schmidt…

Q: If we divide the polynomial P by the factor x - c and we obtain the equation P(x) = (x – c)Q(x) +…

A: we know that if we divide the polynomial px by the factor x-c and we obtain the equation…

Q: Mrs. Allard asked her students to identify which of the polynomials below are in standard form and…

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Q: 9.(T) Decide whether each polynomial has (x + y) as one of its factors. Justify your decision.(2.5)…

A: We decide whether each given polynomial has (x+y) as one of its factors.

Q: Rewie the polynomial in the form ax+ bx+c and then identify the val b, and c 9x – a2 8. - - -

A: Identify the value of a,b,c

Q: 3. Which polynomial expresses the product of 4y(3y² +7y – 11)? O A. 12y³ + 7y – 11 о в. 12у3 + 28у —…

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Q: determine the degree of the given polynomials. 5y6 + y4 - 2y2 - 8

A: The given polynomial is 5y6+y4-2y2-8

Q: Prove that 2r +1 is not a factor of 4r +r - 1.

A: We have to prove that  2x+1 is not a factor of  4x3+x-1.

Q: 4. Which of the following describes the end behavior of the polynomial y = –x³ + x? %3D as z -oo, y…

A: Here  function is given and we have to find the end behavior of function

Q: 43. Which polynomial represents the product of 2x – 3 an- x² + 6x – 2? ® 2x + 6x – 6 - © 21 – 18x –-…

A: Given query is to find the product if the expression.