How do you factor the expression $4 x^{2} + 16 x + 15$ $4x^2 + 16x + 15$ ?

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Answer 1 · 2015-12-30T18:30:50

$4 x^{2} + 16 x + 15 = (2 x + 3) (2 x + 5)$ $4x^2+16x+15=(2x+3)(2x+5)$

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 $x^{2}$ $x^2$ with the constant. We get:

$4 \cdot 15 = 60$ $4*15=60$

Now, we need to find the pair of factors of $60$ $60$ whose sum or difference will give us the coefficient of $x$ $x$ , i.e., $16$ $16$ .

$60$ $60$ 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 $16$ $16$ .

Great! So now we split the coefficient of middle term $(16)$ $(16)$ as a sum of $6$ $6$ and $10$ $10$ as:

$4 x^{2} + (6 + 10) x + 15$ $4x^2 + (6+10)x + 15$
$4 x^{2} + 6 x + 10 x + 15$ $4x^2 + 6x + 10x + 15$

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

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

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

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

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

and voila, that's the factored expression!

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