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
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x.
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
x + 1
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 remainder (without divisions) on dividing f(x) by x – 2, where f(x) = 2x3 – 7x2 + 3
When 2x3 – x2 – 3x + 5 is divided by 2x + 1, then the remainder is
If on dividing 4x2 – 3kx + 5 by x + 2, the remainder is – 3 then the value of k is
If x + 1 is a factor of 3x3 + kx2 + 7x + 4, then the value of k is
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
If x25 + x24 is divided by (x + 1), the result is ______.
