# How do you find the remainder when f(x)=x^3+5x^2-12x+14; x-7?

Jun 26, 2018

See explanation.

#### Explanation:

To find a reminder of a quotient $\frac{P \left(x\right)}{x - a}$ you have to calculate $P \left(a\right)$

$P \left(7\right) = {7}^{3} + 5 \cdot {7}^{2} - 12 \cdot 7 + 14 = 343 + 245 - 84 + 14 = 208$

The reminder is $208$.