Question

(x+2) is one of the factors of the polynomial x³+13x²+32x+20. Find its remaining factors.

A little help....​

Answer 1

x^2+11x+10

or

(x+1)(x+10) since you can factor x^2+11x+10

Explanation:

Let's do synthetic division.

We are dividing by x+2, so -2 will be on the outside. Like this:

-2 | 1 13 32 20

| -2 -22 -20

|___________________________

1 11 10 0

The remainder is 0, so (x+2) is indeed a factor of x^3+13x^2+32x+20.

The other factor we found by doing this is (x^2+11x+10).

You can find more factors by factoring x^2+11x+10.

Two numbers that multiply to be 10 and add to be 11 is 10 and 1 so the factored form of x^2+11x+10 is (x+10)(x+1).