Question

State if the given binomial is a factor of the given polynomial
`(10x ^(3) + 95x^(2) + 40x - 45) / (x + 9)`

Answer 1

The given binomial(x + 9) is a factor of the given polynomial by Factor Theorem

Step-by-step explanation:

Given the below polynomial;

`f(x)=10x^3+95x^2+40x-45`

We're asked to state if the binomial (x + 9) is a factor of the above polynomial.

To do that, we have to apply the Factor Theorem, which states that if f(x) is a polynomial function, then (x - c) is a factor of f(x) if and only if f(c) = 0.

So let's go ahead and determine f(-9);

`\begin{gathered} f(-9)=10(-9)^3+95(-9)^2+40(-9)-45 \\ =-7290+7695-360-45 \\ =0 \end{gathered}`

Since f(-9) is 0, therefore by Factor Theorem, (x + 9) is a factor of the polynomial.