Advertisements
Advertisements
प्रश्न
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
x + 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(–1)3 + 3(–1)2 – 5(–1) – 6
= –2 + 3 + 5 – 6
= 0
Thus, (x + 1) is a factor of the polynomial f(x).
APPEARS IN
संबंधित प्रश्न
Use Remainder theorem to factorize the following polynomial:
`2x^3 + 3x^2 - 9x - 10`
The expression 2x3 + ax2 + bx – 2 leaves remainder 7 and 0 when divided by 2x – 3 and x + 2 respectively. Calculate the values of a and b.
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 − 19x + 6
Using the Remainder Theorem, factorise the following completely:
4x3 + 7x2 – 36x – 63
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(x2 − 7x + 9) ; (x + 1)
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).
What number should be added to 2x3 - 3x2 + 7x -8 so that the resulting polynomial is exactly divisible by (x-1) ?
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x + 2
What number must be added to 2x3 – 7x2 + 2x so that the resulting polynomial leaves the remainder – 2 when divided by 2x – 3?
Find the remainder when 2x3 – 3x2 + 4x + 7 is divided by 2x + 1
