Find the remainder when $x^{3} + 3 x^{2} + 3 x + 1$ is divided by the following Linear polynomials:
$5 + 2 x$

Open in App

Solution

Given polynomial $x^{3} + 3 x^{2} + 3 x + 1$ divided by $5 + 2 x$
If divided by $5 + 2 x$ then $5 + 2 x = 0$ or $x = - \frac{5}{2}$
Replace x by $- \frac{5}{2}$ we get
$p (x) = x^{3} + 3 x^{2} + 3 x + 1$
$p (- \frac{5}{2}) = {(- \frac{5}{2})}^{3} + 3 {(- \frac{5}{2})}^{2} + 3 (- \frac{5}{2}) + 1$
$\Rightarrow p (- \frac{5}{2}) = - \frac{125}{8} + \frac{75}{4} - \frac{15}{2} + 1$
$\Rightarrow (- \frac{5}{2}) = \frac{- 125 + 150 - 60 + 8}{8} = \frac{- 27}{8}$

Suggest Corrections

Similar questions

x^{3} + 3 x^{2} + 3 x + 1

5 + 2 x

Find the remainder when the polynomial $x^{3} + 3 x^{2} + 3 x + 1$ is divided by
$(x - \frac{1}{2})$ .

x^{3} + 3 x^{2} + 3 x + 1

x + 1,

The remainder when the polynomial p(x)= x³ – 3x² + 2x – 1 is divided by x-2 is

Join BYJU'S Learning Program