Question

Can someone explain Remainder Theorem to me?

Answer 1

`P = DQ + R`

`D(x_0) = 0`

Explanation:

`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

Remainder theorem states that;

Explanation:

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

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

• 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 `(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..