Question

select all polynomials that have (x+2) as a factor

Answer 1

Answer: A and C

Explanation:
The factor for A is x(x-5)(x+2)

The factor for C is (x-5)(x+2)(x+1)

Answer 2

The polynomials that have (x+2) as a factor are $\rm A(x) = x^3-3x^2-10x$ and $\rm C(x) = x^3-2x^2-13x-10$ and this can be determined by using the factorization method.

Check all the options in order to determine the polynomials that have (x+2) as a factor.

A)

$\rm A(x) = x^3-3x^2-10x$

Factorize the above equation.

$\rm A(x) = x(x^2-3x-10)$

$\rm A(x) = x(x^2-5x+2x-10)$

$\rm A(x) = x(x(x-5)+2(x-5))$

$\rm A(x) = (x)(x+2)(x-5)$

This polynomial has a factor (x+2). Therefore, this option is correct.

B)

$\rm B(x) = x^3+5x^2+4x$

Factorize the above equation.

$\rm B(x) = x(x^2+5x+4)$

$\rm B(x) = x(x^2+4x+x+4)$

$\rm B(x) = x(x(x+4)+1(x+4))$

$\rm B(x) = (x)(x+1)(x+4)$

Therefore, this option is incorrect.

C)

$\rm C(x) = x^3-2x^2-13x-10$

Factorize the above equation.  

$\rm C(x) = x^3+2x^2-4x^2-8x-5x-10$

$\rm C(x) = x^2(x+2)-4x(x+2)-5(x+2)$

$\rm C(x) = (x^2-4x-5)(x+2)$

This polynomial has a factor (x+2). Therefore, this option is correct.

D)

$\rm D(x) = x^3-6x^2+11x-6$

Factorize the above equation.  

$\rm D(x) = x^3+2x^2-8x^2-16x+27x+54-60$

In the above polynomial (x+2) is not the factor. Therefore, this option is incorrect.

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https://brainly.com/question/6810544