Question

Select the two binomials that are factors of this trinomial x^2+10x+16

A: x+8
B: x+6
C: x+2
D: X-2

Answer 1

Answer: x+6 x+2

tell me if I’m wrong because I put x+8 and x+2 and got it wrong it told me it was x+6 and x+2

Answer 2

The correct options are A: x+8 and C: x+2.

Explanation:

We are given the following expression and we are to factorize it:

`x^2+10x+16`

We are to find such factors that when multiplied they give a result of 16 (1 x 16 = 16) and when added they give a result of 10.

The two such factors of 16 are positive 2 and positive 8.

Factorizing the given expression to get:

`x^2+10+16\\\\x^2+2x+8x+16\\\\x(x+2)+8(x+2)\\\\(x+2)(x+8)`

Therefore, the two binomial factors of the given expression
`x^2+10x+16` are (x+8) and (x+2).