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Annette [7]
4 years ago
14

X^3 + 8 = (x+2)(____) What do I have to multiply by (x+2) to get x^3 + 8

Mathematics
1 answer:
sasho [114]4 years ago
7 0
                  x² -  2x + 4
x + 2|x³ + 0x² + 0x + 8
        x³ + 2x²
               -2x² + 0x
               -2x² -  4x
                          4x + 8
                          4x + 8
                                  0

x³ + 8 = (x + 2)(x² - 2x + 4)
x³ + 8 = (x + 2)(x - 2)(x - 2)
x³ + 8 = (x + 2)(x - 2)²
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Answer:

2x^3-3x^2-10x+15\\

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To find (fg)(x), we have to look at f(x) and g(x) and multiply the two quantities together. We are already given the two quantities individually so all that is left is the multiplication:

(fg)(x)=(-2x+3)(5-x^2)=-10x+2x^3+15-3x^2\\

If we reorder the terms to go from highest degree to lowest, we get our final answer to be the following:

2x^3-3x^2-10x+15

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