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6. On dividing a polynomial p(x) by g(x) if the quotient and the remainder are found to be x and 3
respectively, then find p(x). g(x) is given below
g(x) =
x2 – 4.
Answers
Step-by-step explanation:
Given : a polynomial p(x) divided by x² - 4 , Quotient = x & remainder = 3
To find : Polynomial p(x)
Solution:
As we know that
p(x) = q(x) . g(x) + r(x)
where
q(x) = x
g(x) = x² - 4
r(x) = 3
Substituting all known values
p(x) = x . (x² - 4) + 3
=> p(x) = x³ - 4x + 3
Polynomial p(x) = x³ - 4x + 3 which on dividing by x² - 4 give Quotient x & remainder = 3
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