What is x^3-6x^2-x+30 divided by 4x-1?
Please help x
take out 1/4 and try
no way :( 4x-1 not a factor of
4x^3 -24 x^2 - 4 x + 120
where did you find this problem?
My tutor gave it me
To divide a polynomial by another polynomial, you can use the long division method. Here's how you can do it step by step:
Step 1: Write the dividend (the polynomial being divided) and the divisor (the polynomial you are dividing by) in the proper order:
x^3 - 6x^2 - x + 30
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4x - 1 |
Step 2: Divide the first term of the dividend by the first term of the divisor. In this case, the first term of the dividend is x^3, and the first term of the divisor is 4x. The result is x^2.
x^2
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4x - 1 | x^3 - 6x^2 - x + 30
Step 3: Multiply the divisor (4x - 1) by the result (x^2), and write the product below the dividend. Then, subtract the product from the dividend:
x^2
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4x - 1 | x^3 - 6x^2 - x + 30
- (x^3 - x^2)
- 5x^2 - x + 30
Step 4: Bring down the next term of the dividend, which is - 5x^2:
x^2 - 5x^2
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4x - 1 | x^3 - 6x^2 - x + 30
- (x^3 - x^2)
- 5x^2 - x + 30
Step 5: Divide the first term of the new dividend (- 5x^2) by the first term of the divisor (4x). The result is - (5/4) times x.
x^2 - (5/4)x
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4x - 1 | x^3 - 6x^2 - x + 30
- (x^3 - x^2)
- 5x^2 - x + 30
Step 6: Multiply the divisor (4x - 1) by the result (- (5/4)x), and write the product below the dividend. Then, subtract the product from the dividend:
x^2 - (5/4)x
_______________________
4x - 1 | x^3 - 6x^2 - x + 30
- (x^3 - x^2)
- 5x^2 - x + 30
- (- (5/4)x^2 + (5/4)x)
- (5/4)x - x + 30
Step 7: Bring down the next term of the dividend, which is - (5/4)x:
x^2 - (5/4)x - (5/4)x
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4x - 1 | x^3 - 6x^2 - x + 30
- (x^3 - x^2)
- 5x^2 - x + 30
- (- (5/4)x^2 + (5/4)x)
- (5/4)x - x + 30
Step 8: Divide the first term of the new dividend (- (5/4)x) by the first term of the divisor (4x). The result is - (5/16).
x^2 - (5/4)x - (5/4)x - (5/16)
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4x - 1 | x^3 - 6x^2 - x + 30
- (x^3 - x^2)
- 5x^2 - x + 30
- (- (5/4)x^2 + (5/4)x)
- (5/4)x - x + 30
- (- (5/4)x - (5/16))
30 - (5/16)
Step 9: Since there are no more terms to bring down, the division is complete. The quotient is x^2 - (5/4)x - (5/4)x - (5/16), and the remainder is 30 - (5/16).
Therefore, the division of x^3 - 6x^2 - x + 30 by 4x - 1 is equal to the quotient x^2 - (5/4)x - (5/4)x - (5/16), with a remainder of 30 - (5/16).