# Using remainder theorem find the remainder when 7x³+40x²+22x-35is divided by( x+1)?

Jan 8, 2018

remainder = $- 24$

#### Explanation:

Given: $\frac{7 {x}^{3} + 40 {x}^{2} + 22 x - 35}{x + 1}$

The Remainder Theorem states that when you divide a polynomial $f \left(x\right)$ by a linear factor $\left(x - a\right)$, you will have a quotient function $q \left(x\right)$ and a remainder.

The remainder $= f \left(a\right)$. This remainder can be found using long division, synthetic division or the Remainder Theorem.

Long Division:
" "ul(" "7x^2 + 33x - 11)larr quotient function
$x + 1 | 7 {x}^{3} + 40 {x}^{2} + 22 x - 35$
$\text{ } \underline{7 {x}^{3} + 7 {x}^{2}}$
$\text{ } 33 {x}^{2} + 22 x$
$\text{ } \underline{33 {x}^{2} + 33 x}$
$\text{ } - 11 x - 35$
$\text{ } \underline{- 11 x - 11}$
$\text{ } - 24 \leftarrow$remainder

Remainder Theorem:

linear factor: $\left(x - a\right) = \left(x + 1\right) = \left(x - - 1\right)$.

This means $a = - 1$

$f \left(x\right) = 7 {x}^{3} + 40 {x}^{2} + 22 x - 35$

$f \left(- 1\right) = 7 {\left(- 1\right)}^{3} + 40 {\left(- 1\right)}^{2} + 22 \left(- 1\right) - 35 = - 24$

Remainder $= - 24$