Question

How do you factor `7a^2 + 17a + 6`?

Answer 1

completing the square
(7a+3)(a+2)

Explanation:

`7a^2 +17a+6`

using completing the square method i am writing the middle term in such a way that you get following two things
1. when you multiply these two terms you get the product of first and second term
2. when you add these terms you get the middle term again

`7a^2 +14a +3a+6`

now taking out common terms

`7a(a+2)+3(a+2)`

now again taking out (a+2) common

`(7a+3)(a+2)`

Answer 2

`7a^2+17a+6 = (7a+3)(a+2)`

Explanation:

Let `A=7`, `B=17` and `C=6` represent the coefficients.

Look for a pair of factors of `AC = 7*6 = 42` whose sum is `B=17`.

The pair `B1=3`, `B2=14` works.

Then for each of the pairs `(A,B1)` and `(A,B2)`, divide by the HCF (highest common factor) to get the coefficients of a factor of our quadratic:

`(A,B1) = (7,3) -> (7,3) -> (7a+3)`
`(A,B2) = (7,14) -> (1,2) -> (a+2)`