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astraxan [27]
3 years ago
8

If f(x)=x^3-9x^2+11x+21f(x)=x 3 −9x 2 +11x+21 and x-3x−3 is a factor of f(x)f(x), then find all of the zeros of f(x)f(x) algebra

ically.

Mathematics
1 answer:
Ivanshal [37]3 years ago
6 0

Answer:

x = -1, 3, and 7

Step-by-step explanation:

Using grouping:

f(x) = x³ − 9x² + 11x + 21

f(x) = x³ − 9x² + 18x − 7x + 21

f(x) = x (x² − 9x + 18) − 7 (x − 3)

f(x) = x (x − 6) (x − 3) − 7 (x − 3)

f(x) = (x² − 6x) (x − 3) − 7 (x − 3)

f(x) = (x² − 6x − 7) (x − 3)

f(x) = (x + 1) (x − 7) (x − 3)

To use long division, see the picture.

The zeros are x = -1, 3, and 7.

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