Question

Explain, in complete sentences, how you would completely factor 20x2 – 28x – 48 by using the grouping method. How would you check your factors for accuracy?

Answer 1

take out a factor of four

Answer 2

20x^2-28x-48*

Answer 3

First of all, as you can see you can take out 4 as common from all the terms...
Just do that..

Answer 4

I alredy did @UR. It's just the next part which I'm stuck on. I got 4(x^2-7x-12).

Answer 5

See, what is c here??

Compare it with the standard equation:

Answer 6

4(5x^2-7x-12)

Answer 7

Sry, that was a typo. Now that we have the GCF factored out, Idk what to do really.

Answer 8

now you can see 5 is a prime number so it must be a coefficient of one of the x's in the brackets in the next step

Answer 9

\[4(5x^2-7x-12)=4(5x+...)(x+...)\]

Answer 10

ax^2 + bx^2 + c

Tell me what is the value of c there??

Answer 11

@water it's -12. and I see UR.

Answer 12

No factors of -12 fulfill this.

Answer 13

Oh really very sorry..
a is not 1 it is 5..

just multiply a and c : ac = 5*(-12) = -60

Now guess two numbers with product = -60 and sum = -7

See, I explain you:

When a = 1, then we make the factors of c
When a not equal to one then we make the factors of ac..

Getting this point??
just make the factors of -60 which should produce the sum = -7 and product = -60..

Answer 14

I get it.

Answer 15

As, this one is easy..
two numbers will be 12 and 5..
But we should need product = -60

When their product is -60??
When one of the number must be negative..

So either 12 can be negative or you can take 5 as negative..

But the other condition says that their sum should be -7..
With 12 and 5 how can you get sum = -7

It will only be possible if 12 is negative and 5 is positive so that -12 + 5 = -7


Got till here?