Can #y=x^2 + 10x + 21 # be factored? If so what are the factors ?

2 Answers
Dec 13, 2015

Answer:

Yes.

Explanation:

Yes.

#color(white)(xx)y=x^2+10x+21<=>y=(x+3)(x+7)#

Dec 13, 2015

Answer:

#(x+3)(x+7)#

Explanation:

To look for the factored form of a polynomial, look for the numbers whose product is the final number and whose sum is the middle constant.

The possible pairs of numbers whose product is #21# are:

#1,21#

#3,7#

The sum of #3# and #7# are #10#, which is the middle term of the polynomial.

Thus, we can factor #x^2+10x+21# into #(x+3)(x+7)#.

A good way to check your work is to redistribute the factored form.

#(x+3)(x+7)=x^2+7x+3x+21=x^2+10x+21#