Advertisements
Advertisements
Question
For what value of m is x3 – 2mx2 + 16 divisible by x + 2?
Advertisements
Solution
Let p(x) = x3 – 2mx2 + 16
Since, p(x) is divisible by (x + 2), then remainder = 0
P(–2) = 0
⇒ (–2)3 – 2m(–2)2 + 16 = 0
⇒ – 8 – 8m + 16 = 0
⇒ 8 = 8m
m = 1
Hence, the value of m is 1.
APPEARS IN
RELATED QUESTIONS
What must be subtracted from 16x3 – 8x2 + 4x + 7 so that the resulting expression has 2x + 1 as a factor?
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
x + 2
The polynomials 2x3 – 7x2 + ax – 6 and x3 – 8x2 + (2a + 1)x – 16 leaves the same remainder when divided by x – 2. Find the value of ‘a’.
Using the Remainder Theorem, factorise the following completely:
x3 + x2 – 4x – 4
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
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
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
