Verify the division algorithm for the polynomials.
p(x)= 2x power 4 - 6x power 3 + 2x² - x + 2 and g(x)= x + 2. with proper method and proper solve.
class 9th chapter 2.
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sorry i dont know the answer see from google
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The division of p(x)=x3−1 by g(x)=x−1 is as shown above:
Now we know that the division algorithm states that:
Dividend=(Divisor×quotient)+Remainder
Here, the dividend is x3−1, the divisor is x−1, the quotient is x2+x+1 and the remainder is 0, therefore,
x3−1=[(x−1)(x2+x+1)]+0⇒x3−1=[x(x2+x+1)−1(x2+x+1)]+0⇒x3−1=x3+x2+x−x2−x−1+0⇒x3−1=x3+x2−x2+x−x−1⇒x3−1=x3−1
Hence, the division algorithm is verified.
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