Question

Is the binomial a factor of the polynomial function?

Answer 1

Answer:

Yes, the binomial is a factor of the polynomial function.

Step-by-step explanation:

Consider the given polynomial.

Factor out the common term $x^2$ from the first two terms and $-25$ from the last two terms.

$x^3 + 3x^2 -25x-75=x^2(x+3)-25(x+3)$

Factor out the polynomial.

$x^2(x+3)-25(x+3)=(x+3)(x^2-25)$

Further, simplify.

$(x+3)(x^2-25)=(x+3)(x+5)(x-5)$

Therefore, $x^3 + 3x^2 -25x-75=(x+3)(x+5)(x-5)$

A binomial factor is simply a factor with two terms, like (x - a).

Hence, the given polynomial function is binomial as it contains the factor with two terms, like (x - a).