# How do you factor the expression 2x^2 + 5x - 18?

##### 1 Answer
Dec 23, 2015

$\left(x + \frac{9}{2}\right) \cdot \left(x - 2\right)$

#### Explanation:

first make sure the coefficient of ${x}^{2}$ is 1
you can factorize a quadratic polynomial in the form:
${x}^{2} +$(sum of two numbers)$x +$(product of two numbers)
let the two numbers be $a , b$
so, from the equation, we have
$a + b = \frac{5}{2}$ & $a \cdot b = - \frac{18}{2} = - 9$

solve this 2 equation 2 unknown by substituting either $a = - \frac{9}{b}$ or $b = - \frac{9}{a}$ into the eq $a + b = \frac{5}{2}$
on solving you get the two numbers $a$ & $b$ as $\frac{9}{2} , - 2$
now, you can write:
${x}^{2} + \left(- 2 + \frac{9}{2}\right) x + \left(- 2 \cdot \frac{9}{2}\right)$
${x}^{2} - 2 x + \frac{9}{2} x - 9$
$x \left(x - 2\right) + \frac{9}{2} \left(x - 2\right)$
$\left(x - 2\right) \cdot \left(x + \frac{9}{2}\right)$