Advertisements
Advertisements
Question
The remainder, when x3 – x2 + x – 1 is divided by x + 1, is ______.
Options
0
– 4
2
4
Advertisements
Solution
The remainder, when x3 – x2 + x – 1 is divided by x + 1, is – 4.
Explanation:
We know that when f(x) is divided by x – a
Then remainder = f(a)
Let f(x) = x3 – x2 + x – 1
When f(x) is divided by x – (– 1)
Then remainder
= f(– 1)
= (– 1)3 – (– 1)2 – 1 – 1
= – 1 – 1 – 1 – 1
= – 4
RELATED QUESTIONS
Find 'a' if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
The expression 2x3 + ax2 + bx – 2 leaves remainder 7 and 0 when divided by 2x – 3 and x + 2 respectively. Calculate the values of a and b.
What number should be subtracted from x3 + 3x2 – 8x + 14 so that on dividing it by x – 2, the remainder is 10?
When the polynomial x3 + 2x2 – 5ax – 7 is divided by (x – 1), the remainder is A and when the polynomial x3 + ax2 – 12x + 16 is divided by (x + 2), the remainder is B. Find the value of ‘a’ if 2A + B = 0.
A polynomial f(x) when divided by (x - 1) leaves a remainder 3 and when divided by (x - 2) leaves a remainder of 1. Show that when its divided by (x - i)(x - 2), the remainder is (-2x + 5).
Find the remainder (without divisions) on dividing f(x) by x – 2, where f(x) = 5x2 – 1x + 4
Given f(x) = ax2 + bx + 2 and g(x) = bx2 + ax + 1. If x – 2 is a factor of f(x) but leaves the remainder – 15 when it divides g(x), find the values of a and b. With these values of a and b, factorise the expression. f(x) + g(x) + 4x2 + 7x.
Check whether p(x) is a multiple of g(x) or not
p(x) = x3 – 5x2 + 4x – 3, g(x) = x – 2
By remainder theorem, find the remainder when, p(x) is divided by g(x) where, p(x) = 4x3 – 12x2 + 14x – 3; g(x) = 2x – 1
If x51 + 51 is divided by x + 1, the remainder is ______.
