Can someone explain Remainder Theorem to me?

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Answer 1 · 2018-06-12T21:11:05

$P = DQ + R$

$D(x_0) = 0$

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

If $x_0$ is a root of $D(x)$ , then $P(x_0) = R$

Answer 2 · 2018-06-15T13:39:59

Remainder theorem states that;

If a polynomial $f(x)$ is divided by $(ax + b),$ the remainder $R = f(-b/a)$ , which is the value of the polynomial $f(x)$

When;

$x = -b/a$

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

Now for this;

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

Simply let $x - 1 = 0$

$x = 1$

Put $x = 1$ in $f(x)$ 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 $f(x)$ to attain the remainder..