# The polynomial f(x) = x^3 + 3x^2 + ax + b leaves the same remainder when divided by (x – 2) as when divided by (x +1). Find the value of a?

Jun 27, 2017

$a = - 6$

#### Explanation:

$f \left(x\right) = {x}^{3} + 3 {x}^{2} + a x + b$
$f \left(2\right) = {2}^{3} + 3 \cdot {2}^{2} + 2 a + b = {R}_{1}$
${R}_{1} = 2 a + b + 20$
$f \left(- 1\right) = {\left(- 1\right)}^{3} + 3 \cdot {\left(- 1\right)}^{2} - a + b = {R}_{2}$
${R}_{2} = - a + b + 2$
${R}_{1} = {R}_{2}$
$2 a + b + 20 = - a + b + 2$
$3 a = - 18$
$a = - 6$