Divide p(x)= 2x4+13x2-7x3-11x+5 by g(x) = 3+x2-2x and also verify the division Algorithm
Answers
Answer:
Step-by-step explanation:
Given
Divide p(x)= 2x4+13x2-7x3-11x+5 by g(x) = 3+x2-2x and also verify the division Algorithm
ANSWER
x^2 – 2 x + 3)2x^4 – 7 x^3 + 13 x^2 – 11 x + 5 (2 x^2 – 3 x + 1
2x^4 – 4 x^3 + 6x^2
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-3x^3 + 7x^2 – 11 x
-3x^3 + 6x^2 – 9 x subtracting
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x^2 – 2 x + 5
x^2 – 2 x + 3 subtracting
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2
Now quotient = 2 x^2 – 3 x + 1 and remainder = 2
We know that to verify
Dividend = quotient x divisor + remainder
= (2 x^2 – 3 x + 1)(x^2 – 2 x + 3) + 2
= 2 x^4 – 3 x^3 + x^2 – 4 x^3 + 6 x^2 – 2 x + 6 x^2 – 9 x + 3 + 2
= 2 x^4 – 7 x^3 + 13 x^2 – 7 x^3 – 11 x + 5 (verified)