Question

Chase wants to factor x2 + 10x + 25 by grouping; however, Paige says it is a special product and can factor a different way. Using complete sentences, explain and demonstrate how both methods will result in the same factors.

Answer 1

I keep forgetting how to split the middle term.

Answer 2

@superhelp101

Answer 3

To get quadratics of the form x^2+ax+b in the form (x+c)(x+d) we need to find a c and d such that:

c*d=b
c+d=a

In this case we need to find
c*d=25
c+d=10

Can you find a combination of c and d which satisfy those equations?

Answer 4

this is a perfect square trinomial so it would factor like (x+5)(x+5)

because what numbers multiply to get 25 and add to get 10. That would x+5

Answer 5

Do I look at factors of 25 or 10?

Answer 6

that one was a special products (x+5)^2

Answer 7

factors of 25 are 5 and 5 so the numbers 5 and 5 multiply to get 25 and they also add to get 10. That is what we are looking for

Answer 8

So how do I do the factor by grouping way

Answer 9

um that's the only way I was taught @tom982 do you think you know

Answer 10

After a quick Google I know what you mean by a 'grouping way' now.

\[x^2+10x+25 = (x^2+5x) + (5x+25) = x(x+5)+5(x+5) = (x+5)(x+5)\]

Answer 11

Thank you so much. I don't know why I keep forgetting how to split the middle term.

Answer 12

No problemo, happy to help!