Question

How do you factor `2(x^2) + 9x + 7`?

Answer 1

`2(x^2)` is just `2x^2`
so
`2x^2 +9x +7`
We know seven is a prime number so its only factors are 7 and 1 therefore we know our final answer will look something like this:
(?x+7)(?x+1)

We also know that 2 is a prime number therefore our x coefficients will be 2 and 1.

we know that `2x` x 1 =`2x`
and `1x` x7 = `7x`
so to get our `9x` we can just add `2x` and `7x`

So to times 7 by 1 we put 1 in the opposite bracket, and then do the same for 1 and 2.

So the final answer is:
(2x+7)(x+1)

Answer 2

`y = 2x^2 + 9x + 7`
Since a - b + c = 0, use shortcut.
a. One real root x = -1 --> factor (x + 1)
b. One real roots `x = - c/a = - 7/2` --> factor `(x + 7/2)`
Factored form of y --> y = a(x - x1)(x - x2)
`y = 2(x + 7/2)(x + 1) = (2x + 7)(x + 1)`