The Factor Theorem

Question

Use the Factor Theorem to determine whether x + 3 is a factor of P(x) = x³ + 4x² - 9.Specifically, evaluate P at the proper value, and then determine whether x + 3 is a factor.

Is x+3 a factor of P(x) or not

P(?) = ?

Answer 1

If (x - a) is a factor of the polynomial P(x), then P(a) = 0

For x + 3, use P(x) = P(-3) (x + 3 = 0, x = -3)

P(x) = x³ + 4x² - 9

Then P(-3) = (-3)³ + 4(-3)² - 9 -> -27 + 36 - 9 = 0

So answer is YES.

Answer 2

Mercy,

We say that (x + 1) is a factor of x²+5x+4

because we can "factor" x²+5x+4 into (x+1)(x+4)

This means that whatever number we put into the "original" will equal that same number put into the "factored form"

For example, 10²+50+4 = (10 + 1)(10 + 4)

An easy way to see if something is a factor is to check the zeros

We know that (x+1) is a factor of x²+5x+4 because when x=-1, we have a value of zero (-1+1)=0 (-1)²+-5+4=0

Does this make sense? If so, you should be able to find whether (x+3) is a factor of P(x)

Hope this helps--Andrew F.