Question

How do you factor the trinomial `x^2 + 7x + 10`?

Answer 1

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

Explanation:

Open two sets of brackets. Factors of `x^2` are `x, x`. Since the expressions are positive, both signs will be positive.
`(x+?)(x+?)`

Multiply the first and last coefficients. +1 x +10 = +10.
The factors of +10 are: +1, +10; +2, +5; -2,-5; and -1, -10. Add each.

The second one adds to +7, the middle coefficient. So, +2, and +5 are correct.

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