Solve. (-18x^3+17x+6)/(3x+2)
A. -6x^2+4x+3<------------
B. 6x^2+4x-3
C. -6x^2+4x-3
Dx^2-4x+3
okay
He's right
To solve the expression (-18x^3+17x+6)/(3x+2), we can use long division.
First, divide the first term of the numerator (-18x^3) by the first term of the denominator (3x). The result is -6x^2. Write this as the first term in the quotient.
Next, multiply the divisor (3x+2) by -6x^2 and subtract the product from the numerator. The product is (-6x^2)(3x+2) = -18x^3 - 12x^2. Subtracting this from the numerator (-18x^3+17x+6) gives us:
(-18x^3 + 17x + 6) - (-18x^3 - 12x^2) = 17x + 12x^2 + 6
Now we repeat the process with the new numerator 17x + 12x^2 + 6:
Divide the first term of the new numerator (17x) by the first term of the denominator (3x). The result is 5x. Write this as the second term in the quotient.
Multiply the divisor (3x+2) by 5x and subtract the product from the new numerator. The product is (5x)(3x+2) = 15x^2 + 10x. Subtracting this from the new numerator (17x + 12x^2 + 6) gives us:
(17x + 12x^2 + 6) - (15x^2 + 10x) = 2x^2 + 7x + 6
We repeat the process one last time with the new numerator 2x^2 + 7x + 6:
Divide the first term of the new numerator (2x^2) by the first term of the denominator (3x). The result is (2/3)x. Write this as the third term in the quotient.
Multiply the divisor (3x+2) by (2/3)x and subtract the product from the new numerator. The product is ((2/3)x)(3x+2) = 2x^2 + (4/3)x. Subtracting this from the new numerator (2x^2 + 7x + 6) gives us:
(2x^2 + 7x + 6) - (2x^2 + (4/3)x) = (7/3)x + 6
Now we're left with a new numerator of (7/3)x + 6. Since we cannot divide this by the denominator (3x+2) any further, we have our final quotient:
-6x^2 + 5x + (2/3) + (7/3)x + 2
Simplifying the terms, we get:
-6x^2 + (4x/3) + 3
Therefore, the correct answer is A. -6x^2 + (4x/3) + 3.