Advertisements
Advertisements
Question
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
2x – 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).
Let f(x) = 2x3 + 3x2 – 5x – 6
`f(1/2) = 2(1/2)^3 + 3(1/2)^2 - 5(1/2) - 6`
= `1/4 + 3/4 - 5/2 - 6`
= `-5/2 - 5`
= `(-15)/2 ≠ 0`
Thus, (2x – 1) is not a factor of the polynomial f(x).
APPEARS IN
RELATED QUESTIONS
Find 'a' if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
Find the value of a, if the division of ax3 + 9x2 + 4x – 10 by x + 3 leaves a remainder 5.
Find the values of a and b when the factors of the polynomial f(x)= ax3 + bx2 + x a are (x+3) and (2x-1). Factorize the polynomial completely.
What number should be added to polynomial f(x)= 12x3 + 16x2 - 5x - 8 so that the resulting polynomial is exactly divisible by (2x - 1) ?
The polynomial f(x) = ax4 + x3 + bx2 - 4x + c has (x + 1), (x-2) and (2x - 1) as its factors. Find the values of a,b,c, and remaining factor.
Find the remainder (without division) on dividing 3x2 + 5x – 9 by (3x + 2)
When 2x3 – 9x2 + 10x – p is divided by (x + 1), the remainder is – 24.Find the value of p.
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
Check whether p(x) is a multiple of g(x) or not:
p(x) = 2x3 – 11x2 – 4x + 5, g(x) = 2x + 1
The remainder, when x3 – x2 + x – 1 is divided by x + 1, is ______.
