Question

If $x-2$ is a factor of $x^3-3x+5a$ then find the value of $a.$

• A. $\frac{2}{5}$
• B. $-\frac{4}{5}$
• C. $\frac{4}{5}$
• D. $\frac{1}{5}$

Answer 1

The correct option is C $\frac{4}{5}$

Given that $(x-2)$ is a factor of $x^3-3x+5a$

$\Rightarrow$ Remainder $=0$

$x^2-x-2$

$(x-2))x^3-3x+5a$

$x^3-2x^2$

____________

$0-x^2+5a$

$-x^2+2x$

____________

$0-2x+5a$

$-2x+4$

____________

$+(5a-4)$

____________

$\Rightarrow x^3-3x+5a=(x-2)(x^2-x-2)+(5a-4)$

Remainder $=5a-4$

but it should be zero for $(x-2)$ to be a factor.

$\Rightarrow 5a-4=0$

$a=\frac{4}{5}$

$(x-2)$ will be a factor if a$=\frac{4}{5}$.