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Find the remainder when x4 + 4x2 + 10 is divided by x2 - 2x + 4.
- a)-6
- b)6
- c)4
- d)– 4
Correct answer is option 'A'. Can you explain this answer?
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Find the remainder when x4 + 4x2 + 10 is divided by x2 - 2x + 4.a)-6b)...
To find the remainder when the polynomial x^4 + 4x^2 + 10 is divided by x^2 - 2x + 4, we can use polynomial long division.
x^2 + 2x + 6
___________________________________
x^2 - 2x + 4 | x^4 + 4x^2 + 0x + 10
- (x^4 - 2x^3 + 4x^2)
____________________
6x^3 + 0x^2 + 0x + 10
- (6x^3 - 12x^2 + 24x)
_____________________
12x^2 - 24x + 10
- (12x^2 - 24x + 48)
__________________
-24x - 38
Since the degree of the remainder (-24x - 38) is less than the degree of the divisor (x^2 - 2x + 4), we have found the remainder. The remainder is -24x - 38.
Therefore, the correct answer is (-24x - 38).
x^2 + 2x + 6
___________________________________
x^2 - 2x + 4 | x^4 + 4x^2 + 0x + 10
- (x^4 - 2x^3 + 4x^2)
____________________
6x^3 + 0x^2 + 0x + 10
- (6x^3 - 12x^2 + 24x)
_____________________
12x^2 - 24x + 10
- (12x^2 - 24x + 48)
__________________
-24x - 38
Since the degree of the remainder (-24x - 38) is less than the degree of the divisor (x^2 - 2x + 4), we have found the remainder. The remainder is -24x - 38.
Therefore, the correct answer is (-24x - 38).
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