Advertisements
Advertisements
Question
Find the remainder when x4 + 1 is divided by x + 1.
Advertisements
Solution
By remainder theorem we know that when a polynomial f(x) is divided by x – a, then the remainder is f(a).
f(x) = x4 + 1
Remainder = f(–1)
= (–1)4 + 1
= 1 + 1
= 2
APPEARS IN
RELATED QUESTIONS
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x+1.
Find the remainder when x3 + 3x2 + 3x + 1 is divided by `x - 1/2`
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
2x – 1
Find the remainder when the polynomial f(x) = 2x4 - 6x3 + 2x2 - x + 2 is divided by x + 2.
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x - 4
If x + 1 is a factor of 3x3 + kx2 + 7x + 4, then the value of k is
Check whether p(x) is a multiple of g(x) or not
p(x) = x3 – 5x2 + 4x – 3, g(x) = x – 2
Find the remainder when 3x3 – 4x2 + 7x – 5 is divided by (x + 3)
By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = x3 – 3x2 + 4x + 50, g(x) = x – 3
The polynomial p(x) = x4 – 2x3 + 3x2 – ax + 3a – 7 when divided by x + 1 leaves the remainder 19. Find the values of a. Also find the remainder when p(x) is divided by x + 2.
