What is 3x2 - 2 divided by x plus 1?

Answer 1

3x2 - 2 is a polynomial of order 2.

Therefore, dividing it by (x + 1) will result in a polynomial of order 1. Suppose the quotient is ax + b (where a is non-zero), and with the remainder c.

Thus 3x2 - 2 = (x + 1)*(ax + b) + c

= ax2 + ax + bx + b + c

= ax2 + (a + b)x + (b + c)

Comparing coefficients:

3 = a

0 = a + b => 0 = 3 + b => b = -3

-2 = b + c => -2 = -3 + c => c = 1

Therefore, (3x2 - 2)/(x + 1) = 3x - 3 = 3*(x - 1) and a remainder of 1.