 # How do you factor the trinomial 2x^2+20x+50 ? Priscilla Johnston 2021-12-25 Answered
How do you factor the trinomial $2{x}^{2}+20x+50$ ?
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Explanation:
We see that 2 is a common factor among all of the coefficients so we can factor 2 to the front giving us
$2\left({x}^{2}+10x+25\right)$
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 $5\left(5+5=10,5\cdot 5=25\right)$. So we get
$2\left(x+5\right)\left(x+5\right)=2{\left(x+5\right)}^{2}$

###### Not exactly what you’re looking for? eninsala06
Solution:
Factor 2 out of $2{x}^{2}+20x+50$
$2\left({x}^{2}+10x+25\right)$
Factor using the perfect square rule.
Rewrite 25 as ${5}^{2}$
$2\left({x}^{2}+10x+{5}^{2}\right)$
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
$10x=2\cdot x\cdot 5$
Rewrite the polynomial.
$2\left({x}^{2}+2\cdot x\cdot 5+{5}^{2}\right)$
Factor using the perfect square trinomial rule ${a}^{2}+2ab+{b}^{2}={\left(a+b\right)}^{2}$, where $a=x$ and $b=5$
$2{\left(x+5\right)}^{2}$
###### Not exactly what you’re looking for? karton
Thanks for the clarification, I think it will help me.