Advertisements
Advertisements
Question
x3 − 2x2 − x + 2
Advertisements
Solution
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
RELATED QUESTIONS
Identify polynomials in the following:
`f(x)=4x^3-x^2-3x+7`
If `f(x) = 2x^2 - 13x^2 + 17x + 12` find f(2)
Show that (x + 4) , (x − 3) and (x − 7) are factors of x3 − 6x2 − 19x + 84
Factorize of the following polynomials:
x3 + 13x2 + 31x − 45 given that x + 9 is a factor
If x + 1 is a factor of x3 + a, then write the value of a.
If x − a is a factor of x3 −3x2a + 2a2x + b, then the value of b is
Factorise the following:
(a + b)2 + 9(a + b) + 18
Factorise the following:
`1/x^2 + 1/y^2 + 2/(xy)`
(x + y)(x2 – xy + y2) is equal to
Factorise:
3x3 – x2 – 3x + 1
