Question
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.
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Answered by
GPT 3.5
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)
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)
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