Question

48x^2+34x-40 factor the trinomial? ( 24+ )( 2- )

Answer 1

First, factor a common factor from all three terms.

Answer 2

2?

Answer 3

Yes

Answer 4

and then?

Answer 5

(24x+ )(2x- )?

Answer 6

Then you get
2(24x^2 + 17x - 20)

Answer 7

Now that I wrote the method, let's go over it step by step with your problem.

Answer 8

ok

Answer 9

Your trinomial is 24x^2 + 34x - 20.
When compared to ax^2 + bx + c, you see that you have
a = 24, b = 17, and c = -20.
You follow so far?

Answer 10

yeah

Answer 11

Ok, Now let's multiply ac, so we get
24*(-20) = -480

Answer 12

Now we need two factors of -480 that add up to 17

Answer 13

How about -32 and 15?

Answer 14

yess

Answer 15

Sorry, the other way around. -15 and 32 bec they need to add to +17.

Answer 16

-15*32 = -480
-15 + 32 = 17

Answer 17

okay

Answer 18

Now we factor by parts. That means factor a common factor out of the first two terms, and factor out a common factor out of the last two terms.

Answer 19

We need -15 and 32. Now we rewrite the middle term using these two factors:
24x^2 + 32x - 15x - 20

Answer 20

What do 24x^2 and 32x have in common?

Answer 21

4

Answer 22

4(6x+8)

Answer 23

4 is the number part. What about x?

Answer 24

You're almost there.
4x(6x + 8)

Answer 25

okay

Answer 26

One sec. There is a larger number that can be factored.

Answer 27

8

Answer 28

24x^2 + 32x = 8x(3x + 4)

Answer 29

Good.
Now what can be factored out of the last two terms?
-15x - 20?

Answer 30

-5x(3x+4)

Answer 31

Great. Now let's write everything we have so far, includiong the 2 we originally factored out.

Answer 32

BTW, no x this time
-15x - 20 = -5(3x + 4)

Answer 33

48x^2 + 34x - 40 =
2(24x^2 + 17x - 20) =
2(24x^2 + 32x - 15x - 20) =
2 [ 8x(3x + 4) - 5(3x + 4) ]
The last step now is to pull out the common factor of (3x + 4) inside the brackets:
2 [(3x + 4)(8x - 5) ]
= 2(3x + 4)(8x - 5) (Final answer)

Answer 34

thank you!!

Answer 35

wlcm