Could someone show me how to do this problem..
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?

Question

Could someone show me how to do this problem..
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?

lgbasallote · Answer

factor out 4 first

$$4(5x^2 - 7x - 12)$$ that's better

mertsj · Answer

Then since 5(-12)=-60 and 5+(12) is -7, let's replace -7x with 5x-12x

mertsj · Answer

$$5x^2+5x-12x-12$$

mertsj · Answer

And let's group like this:
$$5x^2+5x-(12x+12)$$
$$5x(x+1)-12(x+1)=(x+1)(5x-12)$$

mertsj · Answer

And not forgetting about the 4 we factored out:
$$4(x+1)(5x-12)$$

mertsj · Answer

And, of course, we would check that by multiplying to make sure we get the original expression.