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

1 answer

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, we can divide g(x) by (x+3):

x^2 - 6x + 8
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x + 3 | x^3 - 3x^2 - 10x + 24
- (x^3 + 3x^2)
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- 6x - 10x
- (-6x - 18)
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8x + 24
- (8x + 24)
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0

The quotient is x^2 - 6x + 8, so g(x) can be factored as (x+3)(x^2 - 6x + 8).