Q7 of 86 Page 42

Find the remainder when f (x) = x4 – 3x2 + 4 is divided by g(x)= x – 2 and verify the result by actual division.

As we know by Remainder Theorem,


If a polynomial p(x) is divided by a linear polynomial (x – a) then, the remainder is p(a)


Therefore, remainder when f(x) is divided by g(x) is f(2)


f(2) = 24 – 3(2)2 + 4


⇒ f(2) = 16 – 12 + 4 = 8


∴ the remainder when x4 – 3x2 + 4 is divided by x – 2 is 8


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