Question

How do you factor the trinomial `5x^2+7x+2`?

Answer 1

(x + 1)(5x + 2)

Explanation:

`y = 5x^2 + 7x + 2`.
Since a - b + c = 0, use shortcut.
The 2 real roots are: x1 = -1 and `x2 = - c/a = - 2/5`.
Therefor, the 2 factors are--> (x + 1) and `(x + 2/5)`
Factored form:
`y = a(x - x1)(x - x2)`
`y = 5( x + 1)(x + 2/5) = (x + 1)(5x + 2)`

Reminder of Shortcut.
a. If a + b + c = 0, the 2 real roots are : 1 and `(c/a)`
b. If a - b + c = 0, the 2 real roots are: - 1 and `(- c/a)`

Answer 2

`(5x+2)(x+1)`

Explanation:

`5x^2 +7x+2`

Find factors of `5 and 2` whose products add to `7`.

We can see that `5+2=7` The other factors are both `1`

`5 xx 1 + 2xx1 = 5+2=7`

`(5x+2)(x+1)`