# How do you factor the expression 4x^2 - 7x - 15?

Mar 21, 2016

$x = \frac{7 \pm 12 \sqrt{2}}{8}$

I will let you finish this off

#### Explanation:

Possible factors of 15 are 1 and 15 or 3 and 5
Possible factors of 4 are 1 and 4 or 2 and 2

Let try

The 15 has to be negative that means that one of the constants is positive and the other is negative

$\left(2 x + 3\right) \left(2 x - 5\right) = 4 {x}^{2} - 10 x + 6 x \textcolor{red}{\ldots \ldots \text{Fail }}$

$\left(4 x + 3\right) \left(x - 5\right) = 4 {x}^{2} - 20 x + 3 x \textcolor{red}{\ldots \ldots \ldots . \text{Fail }}$

$\left(4 x - 15\right) \left(x + 1\right) = 4 {x}^{2} - 15 x + 4 x \textcolor{red}{\ldots \ldots \ldots . . \text{Fail }}$

Looks as though we are going to need to use the formula!

$y = a {x}^{2} + b x + c \text{ " -> " } x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

a=4; b=-7; c=-15

$\implies x = \frac{7 \pm \sqrt{{\left(- 7\right)}^{2} - 4 \left(4\right) \left(- 15\right)}}{2 \left(4\right)}$

$x = \frac{7 \pm \sqrt{288}}{8}$

$x = \frac{7 \pm \sqrt{2 \times {12}^{2}}}{8}$

$x = \frac{7 \pm 12 \sqrt{2}}{8}$

I will let you finish this off
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If you are not sure what you can use to take the root of; use a factor tree. This is the one I built for $\sqrt{288}$. Look for numbers that are squared.