Advertisements
Advertisements
Question
What must be subtracted from the polynomial x3 + x2 – 2x + 1, so that the result is exactly divisible by (x – 3)?
Options
– 31
– 30
30
31
Advertisements
Solution
31
Explanation:
On dividing x3 + x2 – 2x + 1 by (x – 3), we get
Put x = 3, then by remainder theorem
P(3) = 33 + 32 – 2 × 3 + 1
= 27 + 9 – 6 + 1
= 36 – 6 + 1
= 31
So, 31 must be subtracted in order to divide p(x) by (x – 3).
RELATED QUESTIONS
If (x – 2) is a factor of the expression 2x3 + ax2 + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find 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)
Find the values of a and b when the polynomial f(x)= ax3 + 3x2 +bx -3 is exactly divisible by (2x+3) and leaves a remainder -3 when divided by (x+2).
Find the remainder (without division) when 2x3 – 3x2 + 7x – 8 is divided by x – 1 (2000)
When divided by x – 3 the polynomials x3 – px2 + x + 6 and 2x3 – x2 – (p + 3)x – 6 leave the same remainder. Find the value of ‘p’.
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) = x3 – 2x2 – 4x – 1, g(x) = x + 1
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.
The remainder, when x3 – x2 + x – 1 is divided by x + 1, is ______.
