Question

Select all polynomials that have (x-3)(x−3)left parenthesis, x, minus, 3, right parenthesis as a factor. Choose all answers that apply: Choose all answers that apply: (Choice A) A A(x)=x^3-2x^2-4x+3A(x)=x 3 −2x 2 −4x+3A, left parenthesis, x, right parenthesis, equals, x, cubed, minus, 2, x, squared, minus, 4, x, plus, 3 (Choice B) B B(x)=x^3+3x^2-2x-6B(x)=x 3 +3x 2 −2x−6B, left parenthesis, x, right parenthesis, equals, x, cubed, plus, 3, x, squared, minus, 2, x, minus, 6 (Choice C) C C(x)=x^4-2x^3-27C(x)=x 4 −2x 3 −27C, left parenthesis, x, right parenthesis, equals, x, start superscript, 4, end superscript, minus, 2, x, cubed, minus, 27 (Choice D) D D(x)=x^4-20x-21D(x)=x 4 −20x−21

Answer 1

Answer:

  A, C, D

Step-by-step explanation:

One way to answer this question is to use synthetic division to find the remainder from division of the polynomial by (x-3). If the polynomial is written in Horner form, evaluating the polynomial for x=3 is substantially similar.

  A(x) = ((x -2)x -4)x +3

  A(3) = ((3 -2)3 -4)3 +3 = -3 +3 = 0 . . . . . has a factor of (x -3)

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  B(x) = ((x +3)x -2)x -6

  B(3) = ((3 +3)3 -2)3 -6 = (16)3 -6 = 42 . . . (x -3) is not a factor

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  C(x) = (x -2)x^3 -27

  C(3) = (3 -2)3^3 -27 = 0 . . . . . . . . . . . . . has a factor of (x -3)

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  D(x) = (x^3 -20)x -21

  D(3) = (3^3 -20)3 -21 = (7)3 -21 = 0 . . . . has a factor of (x -3)

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The polynomials of choice are A(x), C(x), and D(x).