Divide 12x5 − 36x4 − 6x3 by 6x2
To divide 12x^5 − 36x^4 − 6x^3 by 6x^2, we can use long division:
2x^3 - 6x^2 - x
-----------------
6x^2|12x^5 - 36x^4 - 6x^3
12x^5 - 0 - 2x^3
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- 6x^3
- 6x^3 + 0 + x
----------
- x
Therefore, the answer is:
12x^5 − 36x^4 − 6x^3 divided by 6x^2 = 2x^3 - 6x^2 - x + (-x/6x^2)
Simplifying further, we get:
12x^5 − 36x^4 − 6x^3 ÷ 6x^2 = 2x^3 - 6x^2 - x - (1/6)x
To divide the polynomial 12x^5 - 36x^4 - 6x^3 by 6x^2, we will follow these steps:
Step 1: Divide the coefficient of the first term by the coefficient of the divisor:
12x^5 / 6x^2 = 2x^(5-2) = 2x^3
Step 2: Multiply the result from step 1 by the divisor (6x^2):
2x^3 * 6x^2 = 12x^(3+2) = 12x^5
Step 3: Subtract the result obtained in step 2 from the original polynomial:
(12x^5 - 12x^5) - 36x^4 - 6x^3 = -36x^4 - 6x^3
Step 4: Repeat steps 1-3 with the new polynomial obtained in step 3:
-36x^4 / 6x^2 = -6x^(4-2) = -6x^2
(-6x^2 * 6x^2) - 6x^3 = -36x^4 - 6x^3
Step 5: Subtract the result obtained in step 4 from the new polynomial:
(-36x^4 - 6x^3) - (-36x^4 - 6x^3) = 0
Therefore, the result of dividing 12x^5 - 36x^4 - 6x^3 by 6x^2 is 2x^3 - 6x^2.