Advertisements
Advertisements
प्रश्न
f(x) = x3 −6x2 − 19x + 84, g(x) = x − 7
Advertisements
उत्तर
It is given that f(x) = x3 −6x2 − 19x + 84, and g(x) = x − 7
By the factor theorem, g(x) is the factor of polynomial f(x), if f (7) = 0.
Therefore, in order to prove that (x − 7) is a factor of f(x).
It is sufficient to show that f(7) = 0
Now,
`f(7) = (7)^3 - 6(7)^2 - 19(7) + 84`
` = 343 - 294 - 133 + 84`
` = 427 - 427`
`=0`
Hence, (x − 7) is a factor of polynomial f(x).
APPEARS IN
संबंधित प्रश्न
Write the degrees of each of the following polynomials
`7x3 + 4x2 – 3x + 12`
f(x) = 9x3 − 3x2 + x − 5, g(x) = \[x - \frac{2}{3}\]
Find the remainder when x3 + 3x2 + 3x + 1 is divided by 5 + 2x .
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 cases, if 2R1 − R2 = 0.
For what value of a is (x − 5) a factor of x3 − 3x2 + ax − 10?
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.
When x3 − 2x2 + ax − b is divided by x2 − 2x − 3, the remainder is x − 6. The values of a and b are respectively
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:
12x2 + 36x2y + 27y2x2
