Question

PLEASE HELP!!! <3

Factor the GCF first and then factor the trinomial: 2x^2 + 20x + 50
A. 2(x + 5)(x + 5)
B. 2(x + 5)(x + 10)
C. 2(x + 2)(x + 25)
D. prime

Answer 1

I dont want the answer I need the steps on how to solve the problem (please) :)

Answer 2

With the GFC, you have to look at each number and determine what they have in common; in this case, it would be 2.

Answer 3

What would the equation be after factoring the 2?

Answer 4

Thats about how far I got into the problem was figuring that out, then i wrote it as \[2 \left( x ^{2} + 10x + 25 \right) \] but it looked wrong... Im too used to the grouping method!!

Answer 5

Good! Now, from then, you can factor that trinomial into 2 binomials. Since the 25 is positive, that means we know that the value in both binomials HAVE to both be either positive or negative. However, because the 10 is positive as well, we know that the values have to be positive (if the were negative, the value would be negative as well).

Answer 6

Are you with me so far?

Answer 7

So basically, just break it apart; the factors of 25 are 1:25, 5:5, from these values, which 2 added with result in a 10?

Answer 8

Can you put what youre saying in an equation, i have a hard time following words ..

Answer 9

Of course, no problem.
\[2(x^2+10x+25)\rightarrow 2(x+?)(x+?)\rightarrow 2(x+5)(x+5)\]
If you distribute the (x+5), you'll get:\[2(x^2+10x+25)\]If we use the other factors of 25, 1:25, we would not get the same result:\[2(x+25)(x+1)\neq 2(x^2+10x+25)\]
distribute to find out if you want.