Use the Factor Theorem to factor g(x)=x^3−3x^2−10x+24 into a product of linear factors, given that −3 is a zero of ​g(x).

Question

​g(x)=

Answer 1

To use the Factor Theorem, we know that if -3 is a zero of g(x), then (x+3) is a factor of g(x).

Using long division or synthetic division, divide g(x) by (x+3):

-3 | 1 -3 -10 24
|_______-3____0____-30
1 0 -10 -6

The quotient is 1x^2 + 0x - 10, which can be factored further if possible.

Now, we have the factored form of g(x):

g(x) = (x+3)(x^2 - 10)