Question

solve the problem(divide)​

Answer 1

Answer:

Question :-

$\frac{ {x}^{3} - 1}{ {x}^{2} + x + 1 }$

Solution :-

We first arrange the terms of the dividend and divisor in the decreasing order of their degrees.

Here the divisor is already in the standard form so we arrange the dividend in in standard form.

Standard form :-

The standard form of dividend will be

${x}^{3} + 0 {x}^{2} + 0x - 1$

Step 1 :

To obtain the first term of the quotient divide the highest degree term of the dividend (i.e., x³) by the highest degree term of the divisor (i.e., x²)

$\frac{\cancel {x}^{3} }{\cancel {x}^{2} } = x$

This is x. Then carry out the division process. what remains is - x²- x -1

Step 2 :

Now, to obtain the second term of the quotient, divide the highest degree term of new dividend (i.e., -x² -x -1) by the highest degree term of divisor (i.e., x²).

$\frac{ \cancel-{x}^{2} }{ \cancel{x}^{2} } = - 1$

This gives - 1. Again carry out the division process with - x²- x -1

Step 3 :

What remains is 0.

Note :-

Refer to the attachment