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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)

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ANSWER

[tex](5x - 2) \: and \: (x + 2)[/tex]



EXPLANATION

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

[tex]5 {x}^{2} + 8x - 4[/tex]

We first multiply 5 by -4 to get,

[tex]5 \times ( - 4) = - 20[/tex]

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

[tex] - 2 \: and \: 10[/tex]


We split the middle term with these factors.




[tex]5 {x}^{2} + 10x - 2x - 4[/tex]


We group and factor now to obtain,

[tex]5x(x + 2) - 2(x + 2)[/tex]


We factor again to obtain,

[tex](x + 2)(5x - 2)[/tex]

Therefore the factors to be multiplied are,
[tex](5x - 2) \: and \: (x + 2)[/tex]

Answer:

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

Step-by-step explanation:

Given the trinomial [tex]5x^2+8x-4[/tex]

we have to find the factors of the above trinomial.

[tex]5x^2+8x-4[/tex]

⇒ [tex]5x^2-2x+10x-4[/tex]

⇒ [tex]5x^2-2x+10x-4[/tex]

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

⇒ [tex]x(5x-2)+2(5x-2)[/tex]

⇒ [tex](x+2)(5x-2)[/tex]

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

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