x^2-x-20 divided by x-5
x^2 - x - 20/(x-5) =(x+4)(x-5)/(x-5) = x + 4.
(x^2 - x - 20) / (x-5)
= x+4 , x ≠ 5, that restriction is necessary, as are the brackets
To divide the expression x^2 - x - 20 by x - 5, you can use the long division method. Here's how you can do it step by step:
Step 1: Write the expression you want to divide (x^2 - x - 20) and the divisor (x - 5).
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x - 5 | x^2 - x - 20
Step 2: Divide the first term of the dividend (x^2) by the first term of the divisor (x). Write the result above the line.
x
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x - 5 | x^2 - x - 20
Step 3: Multiply the divisor (x - 5) by the quotient obtained in the previous step (x).
x
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x - 5 | x^2 - x - 20
- (x^2 - 5x)
Step 4: Subtract the product from the dividend.
x
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x - 5 | x^2 - x - 20
- (x^2 - 5x)
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4x - 20
Step 5: Bring down the next term from the dividend (-20).
x + 4
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x - 5 | x^2 - x - 20
- (x^2 - 5x)
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4x - 20
- (4x - 20)
Step 6: Subtract the product from the previous step (4x - 20) from the result of step 5 (4x - 20).
x + 4
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x - 5 | x^2 - x - 20
- (x^2 - 5x)
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4x - 20
- (4x - 20)
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0
Step 7: The division is complete when the degree of the resulting polynomial is lower than the degree of the divisor (x - 5), and the remainder is 0.
Therefore, the result of the division is x + 4, and there is no remainder.