# How do you use the remainder theorem to find the remainder for each division (x^2+2x-15)div(x-3)?

Nov 26, 2016

The remainder $= 0$

#### Explanation:

When we divide a polynomial $f \left(x\right)$ by $\left(x - a\right)$

we get, $f \left(x\right) = \left(x - a\right) q \left(x\right) + r$

If $x = a$

$f \left(a\right) = \left(a - a\right) q \left(x\right) + r$

So, $f \left(a\right) = r$

Here, $f \left(x\right) = {x}^{2} + 2 x - 15$ is divided by $\left(x - 3\right)$

$f \left(3\right) = {3}^{2} + 2 \cdot 3 - 15 = 9 + 6 - 15 = 0$

Remainder $= 0$

$f \left(x\right)$ is divisible by $\left(x - 3\right)$

$\frac{{x}^{2} + 2 x - 15}{x - 3} = \frac{\cancel{x - 3} \left(x + 5\right)}{\cancel{x - 3}}$