Q. 73.9( 34 Votes )

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

Answer :

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) = 2^{4} – 3(2)^{2} + 4

⇒ f(2) = 16 – 12 + 4 = 8

∴ the remainder when x^{4} – 3x^{2} + 4 is divided by x – 2 is 8

Rate this question :

Find the remainder when x^{3} + 3x^{2} + 3x + 1 is divided by the following Linear polynomials:

x + 1

AP- MathematicsFind the remainder when x^{3} + 3x^{2} + 3x + 1 is divided by the following Linear polynomials:

x

AP- MathematicsWhen a polynomial 2x^{3} +3x^{2} + ax + b is divided by (x – 2) leaves remainder 2, and (x + 2) leaves remainder –2. Find a and b.

Find the remainder when x^{3} + 3x^{2} + 3x + 1 is divided by the following Linear polynomials:

AP- Mathematics

Find the remainder when p(x) = x^{3} – 6x^{2} + 14x – 3 is divided by g(x) = 1 – 2x and verify the result by long division.

If the polynomials x^{3} + ax^{2} + 5 and x^{3} – 2x^{2} + a are divided by (x + 2) leave the same remainder, find the value of a.

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

Find the remainder when 9x^{3} – 3x^{2} + x – 5 is divided by