How do you factor the expression 4x^2 + 16x + 154x2+16x+15?

1 Answer
Dec 30, 2015

4x^2+16x+15=(2x+3)(2x+5)4x2+16x+15=(2x+3)(2x+5)

Explanation:

I'm going to explain this using the most common method of factorising: by splitting the middle term.

The first step is to multiply the coefficient of x^2x2 with the constant. We get:

4*15=60415=60

Now, we need to find the pair of factors of 6060 whose sum or difference will give us the coefficient of xx, i.e., 1616.

6060 has the following pairs of factors:

(1,60), (2,30), (3,20), (5,12), (6,10)(1,60),(2,30),(3,20),(5,12),(6,10)

With a quick glance, it's clear that the sum of the factors in the pair (6,10)(6,10) is 1616.

Great! So now we split the coefficient of middle term (16)(16) as a sum of 66 and 1010 as:

4x^2 + (6+10)x + 154x2+(6+10)x+15
4x^2 + 6x + 10x + 154x2+6x+10x+15

Note: It doesn't matter if you reverse the order and split 16x16x as 10x+6x10x+6x, you'll get the same result!

Now, we must take out common factors from the first two terms and then the next two terms:

2x(2x+3)+5(2x+3)2x(2x+3)+5(2x+3)

Now, we can take (2x+3)(2x+3) to be common, to get:

(2x+3)(2x+5)(2x+3)(2x+5)

and voila, that's the factored expression!