When dividing 2x2 - 4x + 5 by (x - 1) the remainder is 11.
True or false
If you mean
(2x^2 - 4x + 5)/(x-1) , the quotient is (2x - 2) with a remainder of 3.
So False is the answer.
To find the remainder when dividing a polynomial, you can use synthetic division or long division. Let's use long division to verify the answer.
To divide 2x^2 - 4x + 5 by (x - 1), first set up the division:
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(x - 1) | 2x^2 - 4x + 5
To begin, divide the first term (2x^2) by (x), which gives you 2x. Then, multiply 2x by (x - 1) and write the result beneath the second term:
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(x - 1) | 2x^2 - 4x + 5
２ｘ^2 - ２ｘ
Next, subtract the second line from the first line:
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(x - 1) | 2x^2 - 4x + 5
２ｘ^2 - ２ｘ
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-2ｘ + 5
Now, divide -2x by (x), which gives you -2. Multiply -2 by (x - 1) and write the result beneath the third term:
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(x - 1) | 2ｘ^2 - 4ｘ + 5
2ｘ^2 - 2ｘ
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-2ｘ + 5
-2ｘ + 2
Again, subtract the lines:
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(x - 1) | 2ｘ^2 - 4ｘ + 5
2ｘ^2 - 2ｘ
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-2ｘ + 5
-2ｘ + 2
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3
The remainder is 3, not 11. Therefore, the statement "When dividing 2x^2 - 4x + 5 by (x - 1) the remainder is 11" is FALSE. The correct statement is "The remainder is 3."