Question

Which factors can be multiplied together to make the trinomial 5x2 + 8x – 4? Check all that apply.

(x + 1)
(2x + 1)
(x + 2)
(5x + 1)
(5x – 2)

Answer 1

The factors are (x+2) and (5x-2). [3 and 5 option]

Explanation:

Given the trinomial
`5x^2+8x-4`

we have to find the factors of the above trinomial.

`5x^2+8x-4`

⇒
`5x^2-2x+10x-4`

⇒
`5x^2-2x+10x-4`

Taking x common from first two terms and 2 common from last two terms.

⇒
`x(5x-2)+2(5x-2)`

⇒
`(x+2)(5x-2)`

hence, the factors which can multiplied to make the trinomial are (x+2) and (5x-2)

Answer 2

ANSWER


`(5x - 2) \: and \: (x + 2)`



EXPLANATION

To determine those factors , we need to factor the quadratic trinomial


`5 {x}^(2) + 8x - 4`

We first multiply 5 by -4 to get,


`5 * ( - 4) = - 20`

Two factors of -20 that will add up to 8 are


`- 2 \: and \: 10`


We split the middle term with these factors.





`5 {x}^(2) + 10x - 2x - 4`


We group and factor now to obtain,


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


We factor again to obtain,


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

Therefore the factors to be multiplied are,

`(5x - 2) \: and \: (x + 2)`