Advertisements
Advertisements
प्रश्न
Using the Remainder and Factor Theorem, factorise the following polynomial:
`x^3 + 10x^2 - 37x + 26`
Advertisements
उत्तर
`f(x) = x^3 + 10x^2 - 37x + 26`
For x = 1
`f(1) = (1)^2 + 10(1)^2 - 37(1) + 26`
= 1 + 10 - 37 + 26
= 0
=> (x - 1) is a factor of `x^3 + 10x^2 - 37x + 26`
Now
Thus by factor theorem
`=> x^3 + 10x^2 - 37x + 26 = (x - 1)(x^2 + 11x - 26)`
`= (x - 1) (x^2 + 13x - 2x - 26)`
`= (x - 1)(x(x + 13) - 2(x + 13))`
`=> x^3 + 10x^2 - 37x + 26 = (x - 1)(x + 13)(x - 2)`
APPEARS IN
संबंधित प्रश्न
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 factorise the following expression:]
`2x^3 + x^2 - 13x + 6`
Find the remainder when x4 + 1 is divided by x + 1.
If (x – 2) is a factor of the expression 2x3 + ax2 + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find the values of a and b.
Using the Remainder Theorem, factorise the following completely:
2x3 + x2 – 13x + 6
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).
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.
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x + `(1)/(2)`.
Using the Remainder Theorem, factorise completely the following polynomial:
3x2 + 2x2 – 19x + 6
By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = x3 – 2x2 – 4x – 1, g(x) = x + 1
