Divide the polynomial 12x^2+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 use long division.

3x + 2
-----------------
4x - 2 | 12x^2 + 2x - 9
- (12x^2 - 6x)
-----------------
8x - 9

Therefore, the quotient is 3x + 2 and the remainder is 8x - 9.

So, the polynomial can be expressed as the product of the divisor and the quotient plus the remainder as:
(4x - 2)(3x + 2) + (8x - 9)