How do you factor the trinomial 2x^2+20x+50 ?

Priscilla Johnston 2021-12-25 Answered

How do you factor the trinomial

2 x^{2} + 20 x + 50

?

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Expert Answer

Serita Dewitt

Answered 2021-12-26 Author has 41 answers

Explanation:
We see that 2 is a common factor among all of the coefficients so we can factor 2 to the front giving us
$2 (x^{2} + 10 x + 25)$
We now need 2 numbers which add to give 10 and multiply to give 25 (or use the quadratic formula). These 2 numbers will be 5 and $5 (5 + 5 = 10, 5 \cdot 5 = 25)$ . So we get
$2 (x + 5) (x + 5) = 2 {(x + 5)}^{2}$

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eninsala06

Answered 2021-12-27 Author has 37 answers

Solution:
Factor 2 out of

2 x^{2} + 20 x + 50

2 (x^{2} + 10 x + 25)

Factor using the perfect square rule.
Rewrite 25 as

5^{2}

2 (x^{2} + 10 x + 5^{2})

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

10 x = 2 \cdot x \cdot 5

Rewrite the polynomial.

2 (x^{2} + 2 \cdot x \cdot 5 + 5^{2})

Factor using the perfect square trinomial rule

a^{2} + 2 a b + b^{2} = {(a + b)}^{2}

, where

a = x

and

b = 5

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

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karton

Answered 2021-12-30 Author has 368 answers

Thanks for the clarification, I think it will help me.

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