Question

x³- x²- 9x - 12 by (x²+ 3x + 3)
Divide the following

Answer 1

Given that,

Dividend [p(x)] = x³ - x² - 9x - 12

Divisor [g(x)] = x² + 3x + 3

Here, we've to divide p(x) by g(x).

Please refer to the above attachment.

First of all, for getting the first term of quotient, we've to divide the first term of dividend and the first term of divisor.

$\Large{\frac{x^3}{x^2}}$

So, it will gives us x.

So, the first term of quotient is x.

Now, we've to multiply x with all the terms of divisor and only to be written under each term of dividend with the same power.

In the attachment you can see that, x is multiplied with x² which is equal to x³ and it's written under x³ only. Similarly 3x^2 and 3x are written under x² and - 9x.

Then we've to subtract each term. For this, we've to change the sign of each term which is written under divisor. Then we've subtract.

Again follow the same procedure.

So here, we'll get quotient as x - 4 and remainder as 0.

$\fbox{\bold{\red{Note:}}}$

Dividend can only be divided by divisor if its degree is greater than the divisor.

You've to stop the division, if the dividend degree is lesser than the divisor and if the remainder comes as 0.