# How do you divide (2x^2+7x-15)div(x+5) using synthetic division?

Jul 15, 2017

$\left(2 x - 3\right)$

#### Explanation:

You can compare coefficients by seeing a quadratic (${x}^{2}$) divided by a linear (single power of x) will result in a linear factor in the form $\left(a x + b\right)$

$2 {x}^{2} + 7 x - 15 = \left(x + 5\right) \left(a x + b\right)$

If you compare coefficients, $x \times a x$ must be $2 {x}^{2}$ so $a = 2$

Similarly, $5 \times b$ must equal $- 15$ so $b = - 3$

I would use algebraic division but I don't know how to do the formatting yet!! I'll update my answer when I find out how to show the 'bus stop method'