loltheresaa
Answered

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)

Verified Answer :

kudzordzifrancis

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,

\(5 \times ( - 4) = - 20\)

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

Answer:

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

Step-by-step 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)

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