Advertisements
Advertisements
प्रश्न
x3 − 2x2 − x + 2
Advertisements
उत्तर
Let `f(x) = x^3 - 2x^2 - x + 2` be the given polynomial.
Now, putting x =1,we get
`f(1) = (1)^3 - 2(1)^2 - (1) + 2`
` = 1-2 - 1+2 = 3 -3`
` = 0`
Therefore, (x+1)is a factor of polynomial f(x).
Now,
`f(x) = x^2 (x-1) -x(x -1) -2(x -1)`
` = (x -1){x^2 - x - 2}`
` = (x -1){x^2 - 2x + x -2}`
` = (x - 1)(x+1)(x - 2)`
Hence (x -1),(x+1) and (x -2)are the factors of polynomial f(x).
APPEARS IN
संबंधित प्रश्न
f(x) = 2x4 − 6x3 + 2x2 − x + 2, g(x) = x + 2
Find the remainder when x3 + 3x2 + 3x + 1 is divided by \[x + \pi\] .
The polynomials ax3 + 3x2 − 3 and 2x3 − 5x + a when divided by (x − 4) leave the remainders R1 and R2 respectively. Find the values of the following case, if R1 + R2 = 0.
If both x + 1 and x − 1 are factors of ax3 + x2 − 2x + b, find the values of a and b.
What must be subtracted from x3 − 6x2 − 15x + 80 so that the result is exactly divisible by x2 + x − 12?
Define zero or root of a polynomial.
If x3 + 6x2 + 4x + k is exactly divisible by x + 2, then k =
If (x − 1) is a factor of polynomial f(x) but not of g(x) , then it must be a factor of
Factorise the following:
p² – 6p – 16
Factorise the following:
(p – q)2 – 6(p – q) – 16
