# Can someone explain Remainder Theorem to me?

Jun 12, 2018

$P = D Q + R$

$D \left({x}_{0}\right) = 0$

#### Explanation:

$P \left(x\right)$ divided by $D \left(x\right)$ equals $Q \left(x\right)$ with remainder $R \left(x\right)$.

If ${x}_{0}$ is a root of $D \left(x\right)$, then $P \left({x}_{0}\right) = R$

Jun 15, 2018

Remainder theorem states that;

#### Explanation:

If a polynomial $f \left(x\right)$ is divided by $\left(a x + b\right) ,$ the remainder $R = f \left(- \frac{b}{a}\right)$, which is the value of the polynomial $f \left(x\right)$

When;

$x = - \frac{b}{a}$

Examples

• Find the positive root of this equation using newton-raphson method to $4$ decimal place

2x³ - 7x² - x + 12

Note: THIS QUESTION IS FROM APPLICATION OF REMAINDER THEOREM

• Find the remainder when 2x³ + 3x - 5 is divided by $\left(x - 1\right)$

• Find the remainder when 2x³ + 3x² - 1 is divided by (x² - x - 2)

Now for this;

Find the remainder when 2x³ + 3x - 5 is divided by $\left(x - 1\right)$

Simply let $x - 1 = 0$

$x = 1$

Put $x = 1$ in $f \left(x\right)$ and what you get is the remainder..

Find the remainder when 2x³ + 3x² - 1 is divided by (x² - x - 2)

Let x² - x - 2 = 0

Solve to get the value of $x$, then substitute in $f \left(x\right)$ to attain the remainder..