Advertisements
Advertisements
प्रश्न
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
2x – 1
Advertisements
उत्तर
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
संबंधित प्रश्न
Find the remainder when x3 + 3x2 + 3x + 1 is divided by `x - 1/2`
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x.
Find the remainder when x3 + 3x2 + 3x + 1 is divided by 5 + 2x.
What must be subtracted from 16x3 – 8x2 + 4x + 7 so that the resulting expression has 2x + 1 as a factor?
What number should be subtracted from the polynomial f(x)= 2x3 - 5x2 +8x -17 so that the resulting polynomial is exactly divisible by (2x - 5)?
use the rernainder theorem to find the factors of ( a-b )3 + (b-c )3 + ( c-a)3
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x - 4
When a polynomial f(x) is divided by (x – 1), the remainder is 5 and when it is,, divided by (x – 2), the remainder is 7. Find – the remainder when it is divided by (x – 1) (x – 2).
For what value of m is x3 – 2mx2 + 16 divisible by x + 2?
What must be subtracted from the polynomial x3 + x2 – 2x + 1, so that the result is exactly divisible by (x – 3)?
