divide using the long division method.
2a^3-12a^2-26a-20/2a-4=-a^3+6a^2+13a+10/a-2
Please help me with the steps because I get the wrong answer.
you appear to "cancel" a two in the numerator and denominator
but the result has most of the signs wrong in the numerator
To divide using the long division method, follow these steps:
Step 1: Write the division problem in long division format:
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2a - 4 | 2a^3 - 12a^2 - 26a - 20
Step 2: Divide the first term of the dividend (2a^3) by the first term of the divisor (2a). The result is the first term of the quotient (-a^2).
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2a - 4 | -a^2
Step 3: Multiply the divisor (2a - 4) by the first term of the quotient (-a^2) and put the result underneath the dividend.
-a^2
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2a - 4 | 2a^3 - 12a^2 - 26a - 20
- (2a^3 - 4a^2)
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- 8a^2 - 26a
Step 4: Subtract the result from the previous step from the dividend. Bring down the next term (-26a).
-a^2
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2a - 4 | 2a^3 - 12a^2 - 26a - 20
- (2a^3 - 4a^2)
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- 8a^2 - 26a
- (-8a^2 + 16a)
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- 10a - 20
Step 5: Divide the first term of the new dividend (-10a) by the first term of the divisor (2a). The result is the next term of the quotient (-5).
-a^2 - 5
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2a - 4 | 2a^3 - 12a^2 - 26a - 20
- (2a^3 - 4a^2)
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- 8a^2 - 26a
- (-8a^2 + 16a)
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-10a - 20
-(-10a + 20)
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0
Step 6: The remainder is 0, which means the division is complete. The quotient is -a^2 - 5.
Therefore, the long division result is:
- a^2 - 5
Please note that this process can be quite complex and daunting. It's essential to maintain careful calculations and double-check each step along the way to avoid errors.