To divide (4x^2 - 2x + 6) by (x - 1) using long division, we start by dividing the highest degree term of the numerator by the highest degree term of the denominator.
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(x - 1) | 4x^2 - 2x + 6
We divide 4x^2 by x, which gives us 4x. Next, we multiply (x - 1) by 4x to get 4x^2 - 4x.
4x
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(x - 1) | 4x^2 - 2x + 6
- (4x^2 - 4x)
We subtract (4x^2 - 4x) from (4x^2 - 2x) to get 2x. We bring down the next term, which is +6.
4x + ?
_______
(x - 1) | 4x^2 - 2x + 6
- (4x^2 - 4x)
__________
2x + 6
Now, we divide 2x by x, which gives us 2. Next, we multiply (x - 1) by 2 to get 2x - 2.
4x + 2
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(x - 1) | 4x^2 - 2x + 6
- (4x^2 - 4x)
__________
2x + 6
- (2x - 2)
We subtract (2x - 2) from (2x + 6) to get 8. Since we have no more terms to bring down, we have completed the long division.
4x + 2
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(x - 1) | 4x^2 - 2x + 6
- (4x^2 - 4x)
__________
2x + 6
- (2x - 2)
__________
8
Therefore, the quotient is 4x + 2 with a remainder of 8.
To check our answer, we can multiply the divisor (x - 1) by the quotient (4x + 2) and add the remainder (8).
(x - 1)(4x + 2) + 8
Expanding the expression, we get:
4x^2 + 2x - 4x - 2 + 8
Combining like terms, we have:
4x^2 + 6
This matches the original numerator, 4x^2 - 2x + 6, confirming that our long division was done correctly.
Divide using long division and then check your answer. (4x^2 - 2x + 6) divided by (x - 1).
The quotient is ? with a remainder of ?
1 answer