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
Identify constant, linear, quadratic and cubic polynomials from the following polynomials
`p(x)=2x^2-x+4`
Verify whether the indicated numbers is zeros of the polynomials corresponding to them in the following case:
\[p(x) = x^3 - 6 x^2 + 11x - 6, x = 1, 2, 3\]
If x = 0 and x = −1 are the roots of the polynomial f(x) =2x3 − 3x2 + ax + b, find the value of a and b.
f(x) = 4x3 − 12x2 + 14x − 3, g(x) 2x − 1
f(x) = x3 − 6x2 + 2x − 4, g(x) = 1 − 2x
If the polynomials ax3 + 3x2 − 13 and 2x3 − 5x + a, when divided by (x − 2) leave the same remainder, find the value of a.
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.
Factorize of the following polynomials:
4x3 + 20x2 + 33x + 18 given that 2x + 3 is a factor.
x4 − 2x3 − 7x2 + 8x + 12
If (x − 1) is a factor of polynomial f(x) but not of g(x) , then it must be a factor of
