Advertisements
Advertisements
Question
Use the Remainder Theorem to factorise the following expression:
2x3 + x2 – 13x + 6
Solution
Let f(x) = 2x3 + x2 – 13x + 6
Factors of 6 are ±1, ±2, ±3, ±6
Let x = 2, then
f(2) = 2(2)3 + (2)2 – 13 × 2 + 6
= 16 + 4 – 26 + 6
= 26 – 26
= 0
∵ f(2) = 0
∴ x – 2 is the factor of f(x) ...(By Remainder Theorem)
Dividing f(x) by x – 2, we get
`x – 2")"overline(2x^3 + x^3 – 13x + 6)("2x^2 + 5x – 3`
2x3 – 4x2
– +
5x2 – 13x
5x2 – 10x
– +
–3x + 6
–3x + 6
– +
x
∴ f(x) = (x – 2)(2x2 + 5x – 3)
= (x – 2)(2x2 + 6x – x – 3)
= (x – 2)(2x(x + 3) – 1(x + 3))
= (x – 2)(2x – 1)(x + 3)
APPEARS IN
RELATED QUESTIONS
Using remainder theorem, find the value of k if on dividing 2x3 + 3x2 – kx + 5 by x – 2, leaves a remainder 7.
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
2x – 1
When x3 + 2x2 – kx + 4 is divided by x – 2, the remainder is k. Find the value of constant k.
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(2x3 − 2x2 + ax − a) ; (x − a)
Polynomials bx2 + x + 5 and bx3 − 2x + 5 are divided by polynomial x - 3 and the remainders are m and n respectively. If m − n = 0 then find the value of b.
Find the values of m and n when the polynomial f(x)= x3 - 2x2 + m x +n has a factor (x+2) and leaves a remainder 9 when divided by (x+1).
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.
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 ‘a’ if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
Find the remainder when 2x3 – 3x2 + 4x + 7 is divided by 2x + 1
