Divide the polynomial 12x2+2x−9 by 4x−2. Then express the polynomial as the product of the divisor and the quotient plus the remainder.

Answer 1

To divide the polynomial 12x^2 + 2x - 9 by 4x - 2, we can use long division:

3x + 2
__________________
4x - 2 | 12x^2 + 2x - 9
- (12x^2 - 6x)
_______________
8x - 9
- (8x - 4)
____________
-5

The quotient is 3x + 2 and the remainder is -5. Thus, the polynomial can be expressed as the product of the divisor and the quotient plus the remainder as:

12x^2 + 2x - 9 = (4x - 2)(3x + 2) - 5