Question

Factor the trinomial 2xsquared + 5x -42

Answer 1

Basic quadratic expression:

`ax^2+bx+c`

`2x^2+5x-42`

Factoring a quadratic expression when a ≠ 0

1. Multiply a and c values (ac=k)

`2(-42) = -84`

2. Find a factor pair whose sum adds to b and has the product of k

`-7,12`

`-7(12)=-84`
`-7+12=+5`

3. Replace the middle term (bx) with newfound values

`2x^2 +12x-7x-42`

4. Factor by grouping

`2x(x+6) -7(x+6)`

• if done correctly the expression in the parentheses will be the same

5. Perform the last factorization

`(2x-7)(x+6)`

• you can verify your answer by expanding the factors to get the same expression in the beginning