Advertisements
Advertisements
Question
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x + 2
Advertisements
Solution
p(x) = 4x3 - 3x2 + 2x - 4 ...(i)
By the remainder theorem the required remainder = p(2).
Put x = -2 in equation (i), we get
p(-2) = 4(-2)3 -3(-2)2 + 2(-2)-4
= 4 x (-8) -3 x 4 -4 -4
= -32 -12 -4 -4
= -52
Hence, the remainder is -52.
RELATED QUESTIONS
When x3 + 2x2 – kx + 4 is divided by x – 2, the remainder is k. Find the value of constant k.
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.
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(54m3 + 18m2 − 27m + 5) ; (m − 3)
What number must be added to 2x3 – 7x2 + 2x so that the resulting polynomial leaves the remainder – 2 when divided by 2x – 3?
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.
If on dividing 2x3 + 6x2 – (2k – 7)x + 5 by x + 3, the remainder is k – 1 then the value of k is
By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial: x4 + 1; x – 1
Check whether p(x) is a multiple of g(x) or not:
p(x) = x3 – 5x2 + 4x – 3, g(x) = x – 2
Determine which of the following polynomials has x – 2 a factor:
4x2 + x – 2
If x25 + x24 is divided by (x + 1), the result is ______.
