Question

factor 4p^2-10p-50

Answer 1

First factor out the GCF (greatest common factor). Do you know how to do that?

Answer 2

yes

Answer 3

that would come out to 2(2p^2-5p-25)

Answer 4

Good. Then there are lots of different methods for factoring that new trinomial. Do you know what method you're familiar with? Guess and check, box and diamond, bottoms up...? Any of those sound familiar?

Answer 5

no

Answer 6

bottoms up? Haha.

Answer 7

Bottoms Up is actually a really cool method for factoring trinomials when a>1. It's a funny name, but it actually makes it much easier!

Answer 8

@candy123456 do you have a lot of these to factor? Or just this one?

Answer 9

like 4

Answer 10

Do you want me to show you the bottoms up method? Or do you want to just guess/check these problems?

Answer 11

whatever is easier

Answer 12

I teach Algebra 2 -- most of my kids prefer the bottoms up method. Once you get the process, it's definitely easier. But if you understand the method behind factoring and FOILing, then guess/check may be quicker. It just depends on what you're comfortable with.

Answer 13

bottoms up sounds good to me

Answer 14

Ok...let me know if you get confused. :)

Answer 15

First step is multiply a by c. So your problem is
a = 2, and c = -25. So slide the 2 over and multiply it by the -25.

Answer 16

Sorry, the equation disappeared in there...

Answer 17

\[2p ^{2}-5p-25\]
becomes
\[p ^{2}-5p-50\]
because we did 2 times the 25...

Answer 18

With me?

Answer 19

yes

Answer 20

Ok now we factor that like a normal trinomial where a=1. Do you know how to do that one?

Answer 21

yes

Answer 22

Ok let me know what you get. 2 steps after that.

Answer 23

(p-1-)(p+5)

Answer 24

sorry (p-10)(p+5)

Answer 25

Good! Now you divide each of those numbers by the original a (the 2, not the 4 -- this gets a little confusing when you factor out a GCF before starting this method...but use the 2). So then we have:
\[(p-\frac{ 10 }{ 2 })(p+\frac{ 5 }{ 2 })\]
This is a strange process, I know...but stick with me, almost done.

Answer 26

Reduce any of the fractions, if possible.

Answer 27

would u reduce the 10/2

Answer 28

Yep. So then you have:
\[(p-5)(p+\frac{ 5 }{ 2 })\]

Answer 29

Last step. You "bottoms up" the factor with a fraction in it. That means you take the denominator (the bottom) and move it UP in front of the variable.
So (p + 5/2) becomes (2p + 5).
I know it's weird, but it works!

Answer 30

With me?

Answer 31

yes so i would get (p+5)(2p+5) ?

Answer 32

Yes! But don't forget to stick the 2 in the very front from when you factored out the GCF. So final answer should be 2(p-5)(2p+5).

Answer 33

oo yeah !

Answer 34

thanks

Answer 35

No problem!