# What is the remainder when you divide 4x3 - 5x2 + 3x - 1 by x - 2?

Dec 16, 2017

Option D) 17

#### Explanation:

We must consider the factor theorem:

$f \left(a\right)$ is the remainder of $f \frac{x}{x - a}$

So hence the remainder of $\frac{4 {x}^{3} - 5 {x}^{2} + 3 x - 1}{x - 2}$ is:

$\left(4 \cdot {\left(2\right)}^{2}\right) - \left(5 \cdot {\left(2\right)}^{2}\right) + \left(3 \cdot 2\right) - 1$

$\implies = 17$

Or you could approach this the long way, via division

Dec 16, 2017

$17 \to \left(D\right)$
$\text{using the "color(blue)"remainder theorem}$
• " the remainder when "f(x)" is divided by "(x-a)" is "f(a)
$\Rightarrow \text{remainder } = 4 {\left(2\right)}^{3} - 5 {\left(2\right)}^{2} + 3 \left(2\right) - 1 = 17$