(3x^3+17x^2+21x-9)/ (x+3)
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To divide (3x^3 + 17x^2 + 21x - 9) by (x + 3), we will use polynomial long division.
We start by dividing the first term of the numerator by the first term of the denominator:
3x^3 / x = 3x^2
Next, we multiply (x + 3) by 3x^2 to get:
3x^2(x + 3) = 3x^3 + 9x^2
Now, we subtract this from the original numerator:
(3x^3 + 17x^2 + 21x - 9) - (3x^3 + 9x^2) = 8x^2 + 21x - 9
Now we repeat the process with the new polynomial, 8x^2 + 21x - 9, and the denominator (x + 3):
8x^2 / x = 8x
8x(x + 3) = 8x^2 + 24x
Subtracting this from our polynomial:
(8x^2 + 21x - 9) - (8x^2 + 24x) = -3x - 9
Now we have a new polynomial, -3x - 9, and we repeat the process:
-3x / x = -3
-3(x + 3) = -3x - 9
Subtracting this from the remainder:
(-3x - 9) - (-3x - 9) = 0
Our final answer is:
3x^2 + 8x - 3
Therefore, (3x^3 + 17x^2 + 21x - 9) / (x + 3) = 3x^2 + 8x - 3.