Use the Remainder Theorem to completely factor p(x) = x 3 + 7x 2 + 11x + 5.

1 answer:

6 0

Let's try (x+5) first. According to the Remainder Theorem, if (x+5) is a factor of the polynomial, the remainder is zero.

when x+5=0, x=-5
use synthetic division:

-5 I 1 7 11 5
I -5 -10 -5
----------------------
1 2 1 0
the remainder is 0, so (x+5) is a factor:
the result is (x+5)(x²+2x+1)
factor again: (x+5)(x+1)(x+1) is the final answer.

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