Question

Sari is teaching her best friend factor trinomials with a leading coefficient greater than 1. She starts with the trinomial 2x^2 + 5x + 3.

Show/describe all of the steps for finding the factorization of the trinomial. Be sure to include the final factorization in your description.

Answer 1

(2x+3)(x+1)

Explanation:

The given trinomial is:

`2 {x}^(2) + 5x + 3`

This trinomial is of the form:

`a {x}^(2) + bx + c`

where a=2, b=5, c=3

We multiply a by c to get

ac=6

Two factors of 6 that sums up to 5 are 2 and 3.

Split the middle term with these factors to get:

`2 {x}^(2) + 2x + 3x + 3`

Factor by grouping

`2x(x + 1) + 3(x + 1)`

`(2x + 3)(x + 1)`