Question

Find the answer using remainder theorem p(x) = x 3 + 7x 2 + 11x + 5

Answer 1

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.