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Which polynomial expression in factored form has 2 as a leading coefficient with −1, 3, and −5 as zeros?

A) 2(x + 1)(x − 3)(x + 5)
B) 2(x − 1)(x + 3)(x − 5)
C) 2x(x + 1)(x − 3)(x + 5)
D) 2x(x − 1)(x + 3)(x − 5)

Respuesta :

Padoru

First, lets find the factors that take the form (x-a), where a is the zero.

-1 is a zero. Thus, [tex](x-(-1))[/tex], aka [tex](x+1)[/tex], is a factor.

3 is a zero. Thus, [tex](x-3)[/tex] is a factor.

-5 is a zero. Thus, [tex](x-(-5))[/tex], aka [tex](x+5)[/tex], is a factor.

Matching these factors with the possible answer choices, we can safely see that either A or C is possible.

x is not a factor because that means the polynomial will have a zero of 0, which is not stated in the question. This eliminates C and D.

This leaves us with answer choice A.

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