Advertisements
Advertisements
प्रश्न
x3 − 3x2 − 9x − 5
Advertisements
उत्तर
Let `f(x) = x^3 - 3x^2 - 9x -5 ` be the given polynomial.
Now, putting x = 1,we get
`f(-1) = (-1)^3 -3(-1)^ -9(-1) - 5`
`=-1 -3 +9 -5 = -9 +9 = 0`
Therefore, (x + 1)is a factor of polynomial f(x).
Now,
`f(x) = x^2 (x+1) -4x(x+1) -5(x +1)`
` = (x+1){x^2 -4x -5}`
` =(x+1){x^2 - 5x + x -5}`
` = (x+1)(x+1)( x-5)`
Hence (x+1) , (x+1) and (x - 5) are the factors of polynomial f(x) .
APPEARS IN
संबंधित प्रश्न
Write the degrees of each of the following polynomials
`7x3 + 4x2 – 3x + 12`
Identify constant, linear, quadratic and cubic polynomials from the following polynomials:
`r(x)=3x^2+4x^2+5x-7`
f(x) = x3 − 6x2 + 2x − 4, g(x) = 1 − 2x
Using factor theorem, factorize each of the following polynomials:
x3 + 6x2 + 11x + 6
x3 − 23x2 + 142x − 120
2x4 − 7x3 − 13x2 + 63x − 45
If \[x = \frac{1}{2}\] is a zero of the polynomial f(x) = 8x3 + ax2 − 4x + 2, find the value of a.
One factor of x4 + x2 − 20 is x2 + 5. The other factor is
(x+1) is a factor of xn + 1 only if
If x + 2a is a factor of x5 – 4a2x3 + 2x + 2a + 3, find a.
