Question

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).
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Answer 1

To use the Factor Theorem, we know that if a polynomial function g(x) has a zero at x = c, then (x - c) is a factor of g(x).

In this case, we are given that -3 is a zero of g(x), so (x + 3) is a factor of g(x).

We can now use synthetic division to divide g(x) by (x + 3):

-3 | 1 -3 -10 24
| -3 18 -24
_______________
1 -6 8 0

The result of the division is x^2 - 6x + 8. Therefore, we have factored g(x) as:

g(x) = (x + 3)(x^2 - 6x + 8)