Divide
36x^3-73x^2-45x-6
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9x + 2
well, 36x^3-73x^2-45x-6 = (9x+2)(4x^2-9x-3)
Or, if you want to do the division manually, enter the polynomials at
http://calc101.com/webMathematica/long-divide.jsp
To divide the polynomial 36x^3-73x^2-45x-6 by the polynomial 9x + 2, we will use polynomial long division. Here's how you can do it:
Step 1: Arrange the terms in descending order of their exponents.
The dividend polynomial is 36x^3-73x^2-45x-6, and the divisor polynomial is 9x + 2. Arrange the terms in descending order:
36x^3 - 73x^2 - 45x - 6 ÷ 9x + 2
Step 2: Divide the first term of the dividend by the first term of the divisor.
Divide 36x^3 by 9x: (36x^3 ÷ 9x) = 4x^2
Step 3: Multiply the whole divisor by the quotient obtained in step 2.
Multiply (9x + 2) by 4x^2: (9x + 2) × 4x^2 = 36x^3 + 8x^2
Step 4: Subtract the product obtained in step 3 from the dividend.
Subtract the result from step 3 from the original dividend:
(36x^3 - 73x^2 - 45x - 6) - (36x^3 + 8x^2) = -73x^2 - 45x - 6 - 8x^2
Step 5: Repeat steps 2-4 until all terms have been processed.
-73x^2 - 45x - 6 - 8x^2 ÷ 9x + 2
Repeat steps 2-4:
Divide -73x^2 by 9x: (-73x^2 ÷ 9x) = -8.11x
Multiply (9x + 2) by -8.11x: (9x + 2) × -8.11x = -73x^2 - 16.22x
Subtract the product obtained in step 3 from the current result:
(-73x^2 - 45x - 6 - 8x^2) - (-73x^2 - 16.22x) = -45x - 6 - 16.22x
Continue performing the steps until no terms remain.
Step 6: Divide -45x by 9x: (-45x ÷ 9x) = -5
Multiply (9x + 2) by -5: (9x + 2) × -5 = -45x - 10
Subtract the product obtained in step 6 from the current result:
(-45x - 6 - 16.22x) - (-45x - 10) = -6 - 16.22x + 10
Simplifying the last step gives us:
-6 - 16.22x + 10 = 4 - 16.22x
Since there are no more terms to divide, the resulting quotient is 4x^2 - 8.11x - 5, and the remainder is 4 - 16.22x.
Therefore, the division of 36x^3-73x^2-45x-6 divided by 9x + 2 is equal to the quotient 4x^2 - 8.11x - 5 with a remainder of 4 - 16.22x.