Use polynomial long division to find the quotient and the remainder when
4x 3 −3x 2 −x−2 is divided by x−4 :
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http://calc101.com/webMathematica/long-divide.jsp
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To use polynomial long division, follow these steps:
Step 1: Write out the dividend and divisor
The dividend is 4x^3 - 3x^2 - x - 2, and the divisor is x - 4.
Step 2: Divide the first term of the dividend by the first term of the divisor
Divide 4x^3 by x to get 4x^2.
Step 3: Multiply the divisor by the quotient obtained in step 2
Multiply x - 4 by 4x^2 to get 4x^3 - 16x^2.
Step 4: Subtract the product obtained in step 3 from the dividend
Subtract 4x^3 - 16x^2 from 4x^3 - 3x^2 - x - 2.
This gives you 13x^2 - x - 2.
Step 5: Bring down the next term from the dividend
Bring down the -x term, which gives you 13x^2 - x.
Step 6: Divide the first term of the new dividend by the first term of the divisor
Divide 13x^2 by x to get 13x.
Step 7: Multiply the divisor by the quotient obtained in step 6
Multiply x - 4 by 13x to get 13x^2 - 52x.
Step 8: Subtract the product obtained in step 7 from the new dividend
Subtract 13x^2 - 52x from 13x^2 - x.
This gives you 51x - 2.
Step 9: Bring down the next term from the new dividend
Bring down the -2 term, which gives you 51x - 2.
Step 10: Divide the first term of the new dividend by the first term of the divisor
Divide 51x by x to get 51.
Step 11: Multiply the divisor by the quotient obtained in step 10
Multiply x - 4 by 51 to get 51x - 204.
Step 12: Subtract the product obtained in step 11 from the new dividend
Subtract 51x - 204 from 51x - 2.
This gives you 202.
Step 13: The quotient is obtained by combining all the quotients obtained in step 2, 6, and 10
The quotient is 4x^2 + 13x + 51.
Step 14: The remainder is the final constant obtained in step 12
The remainder is 202.
Therefore, when 4x^3 - 3x^2 - x - 2 is divided by x - 4, the quotient is 4x^2 + 13x + 51, and the remainder is 202.