Which of the following polynomials has a remainder of 1 when divided by x + 2, x + 3 and x + 5? x³ + 10x² + 31x + 31 None of the above x³ + 10x² + 31x + 29 x³ + 10x² + 31x + 30

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: ) Perform the following division of polynomials by synthetic division. b) (3x* + 10x3 –- 22x² + 14x…

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Q: Is 7x to the 3rd power a polynomials

A: A polynomial is an algebric expression with at least one term in it.Given expression is 7x3. Here…

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: Find the LCM of the given polynomial. x2 - 4,   x2 - x - 2

A: we have to find the LCM of the given Polynomial  f(x)=x2-4p(x)=x2-x-2

Q: Which of the following polynomials is exactly divisible by (3x+1)? A. 6x2+17x+5 B. 9x2+6x+1 C.…

A: We have to check which of the given polynomials is exactly divisible by 3x+1. Factor theorem states…

Q: Perform the following division of polynomials by synthetic division. (x^4 - x^3 - 9x^2 + 29x - 30)…

A: Given:    x4-x3-9x2+29x-30x2-3x+4

Q: Show that (2x+7) is a factor 2x2+5x2-11x-14.Hence factories the given expression completly ,by using…

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Q: 10. Which of the following polynomials is NOT divisible by (3x+ 1)? A. 6x2 + 17x+ 5 B. 3x - 4x2+…

A: Use remainder theorem

Q: Which of the polynomials below is a 3rd degree polynomial? Select one: O a. 3x25x+7 O b. 5x 3-6x4 +…

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Q: 2. Determine if the second polynomial is a factor of the first polynomial. f(x) = 2x' -11x² – 22x+7;…

A: (x-7) will be a factor of f(x) if on dividing f(x) by g(x) ,we get the remainder zero.

Q: 6) Divide the following polynomials a) (2x³ – 3x² + 4x + 5) ÷ (x + 2) b) (16x3 – 12x² + 20x – 3) ÷…

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Q: Find the polynomial to represent (3x-7)2. O 9r2 - 21x + 49 O 9x2 + 21x + 49 9z2 – 42x + 49 9x2 + 42x…

A: We have to find the polynomial which represents the given expression: 3x-72 We know the algebraic…

Q: 2. P(x) = x+ 2x² – 23x-60

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Q: C. Divide the following polynomials using synthetic division. 7. x2-5x +4; x- 1 8. x- 6x - 4; x +2…

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Q: Find for the quotient of the following polynomials using synthetic division. 3. (2x + 3x - 2x + 4) +…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Divide the following polynomials: A.(2x⁵-3x⁴-5x³+5x²+3x-2) by (2x²+x-1)

A: This question is related to divisions of two polynomial..

Q: Which of the following polynomials go to negative infinity as x approaches infinity but go to…

A: Checking option b because  Option a,c,d is positive when x approaches to infinity and negative when…

Q: Do the polynomials x³ + 2x – 4, x³ + x² – 3x + 1, and æ³ + 5 generate P3(R)? Explain. - -

A: Here generate means span.  The span of a set of vectors is the set of all linear combinations of the…

Q: determine the degree of the given polynomials. 5x3y2 - 6x3y3

A: The given polynomial is 5x3y2-6x3y3. Recall, "The degree of a polynomial is the degree of its terms…

Q: The following polynomial has factors (x + 8) and (3x + 2). Determine the value of k. -6x³-55x² + kx…

A: We have a polynomial -6x3-55x2+kx-16 Now, x+8and 3x+2 are the factors. So,  x+8=0 ⇒x=-83x+2=0 ⇒x=-23…

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: determine the degree of the given polynomials. -5x2y2 - 6xy2 + x

A: Consider the provided polynomial, 5x2y2-6xy2+x Determine the degree of the given polynomial.

Q: Which polynomial correctly combines the like terms and expresses the given polynomial in standard…

A: Given: The polynomial expression is 8mn5-2m6+5m2n4-m3n3+n6-4m6+9m2n4-mn5-4m3n3.

Q: Which of the following operations on polynomials will always result in another polynomial? Select…

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Q: 1. Which of these polynomials could have (x - 2) as a factor? Select all that apply. *

A: We have to find which polynomial has a factor (x-2).

Q: For the following polynomial P(x) = ax4 + bx3 + cx2 + 3x − 8 , it has a constant finite difference…

A: Constant finite difference = Degree!×Leading Coefficient-48=4!×a24a=-48a=-2

Q: Add or Subtract the following Polynomials listed on the attached document. 1. (4a - 6a 3a + a + 1) +…

A: Technique to be used:- 1.Write terms having same powers together. 2.Then add or subtract…

Q: Which of the following is not a factor of x^3 + 5x^2 - x - 5? * 5 puntos x + 1 x - 5 x + 5 x - 1…

A: Given the polynomial

Q: Find the least common multiple of the following pair of polynomials:x(x - 1) 2 ( x + 1)  and 4( x -…

A: The least common multiple (LCM) is the smallest quantity which is multiple of more than one…

Q: Find the zeroes of the given polynomials  p(x)=x4-16

A: The polynomial is given as, Px:x4-16 The degree of the given polynomial is four. Therefore, it will…

Q: Find the factors of the following polynomials. 9. x? – 4 10. x2 + 4x-5 11. 3x + 6x² + 5x + 10

A: It is reuquired to find the factors of the given polynomials.

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: Find the greatest common divisor of the polynomials. f(x)= x³-11x²+24x+30 & g(x) = x² - 12x +35.

A: We have to find greatest common divisor of Given polynomial function.

Q: Which of the following polynomial expressions factors into (2x - 6)²? O 4x2 - 24x + 36 O 4x2 + 24x +…

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Q: Add the polynomial (-3x + 4) + (8x - 5) None 5x - 9 11x - 1 11x - 9 5x - 1 of these

A: The two polynomials are and . Addition of two polynomials involves adding the terms of each…

Q: 2. Rewrite the following polynomial in standard form: Sx-4-3x+2.x 3. What is the constant term in…

A: solution Q2 standard form of the polynomial = ax4 + bx3 +cx2 + dx +e

Q: Match each of the following polynomial with whether it is even, odd or neither. - v P(x) = 3x4 -5x²…

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Q: Which of the following polynomials is reducible over Q: x3 +2 x4 + 3 x5 + 1 x2 + 3 I thought it…

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Q: Perform the following division of polynomials by long division. (12x^3 - 7x^2 -38x +42) / (4x - 5)

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Q: Consider the following polynomial. m12,3 - n³z12 (a) Can the polynomial be treated as the difference…

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Q: 2) Perform the following division of polynomials by synthetic division. a) (10x³ – 31x² + 26x –…

A: Given : (10x3-31x2+26x-3)÷(2x-3) While using synthetic division , solve the divisor for x…

Q: 9) Perform the following division of polynomials by synthetic division. (8x3 + 6x² – 39x + 11) ÷ (4x…

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Q: A. Divide the following polynomials using the long method. 4. x² +2x - 8; x – 2 5. x-6x + 12x – 8; x…

A: The long division method is used when you are dividing a large number  by a two-digit  number. It is…

Q: Perform the following division of polynomials by synthetic division. (xª – x³ – 9x² + 29x – 30) ÷…

A: Given information: x4-x3-9x2+29x-30÷(x2-3x+4) Therefore, can be written as, x4-x3-9x2+29x-30x2-3x+4…

Q: II. Find for the quotient of the following polynomials using synthetic division. 3. (2x + 3x-2x + 4)…

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Q: determine the degree of the given polynomials. 7x - 2y

A: Given: 7x-2y

Q: Which polynomial gives a quotient of (3x^2 + 2x + 4) and a remainder of 19 when divided by (2x – 3)?…

A: We have to find polynomial on the basis of given information.

Q: 2) Perform the following division of polynomials by synthetic division. b) (3x* + 10x3 – 22x² + 14x…

A: Consider the given polynomial,   3x4+10x3-22x2+14x-3÷x2+4x-5   Further simplify the polynomial.…

Q: 17) Perform the following division of polynomials by synthetic division. (x* – x³ – 9x² + 29x – 30)…

A: Given (x4-x3-9x2+29x-30) ÷ x2-3x+4

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.