Advertisements
Advertisements
प्रश्न
\[f(x) = 3 x^4 + 2 x^3 - \frac{x^2}{3} - \frac{x}{9} + \frac{2}{27}, g(x) = x + \frac{2}{3}\]
Advertisements
उत्तर
Let us denote the given polynomials as
`f(x) = 3x^4 + 2x^3 - x^2/3 - x/9 + 2/27,`
`g(x) = x+ 2/3`
`⇒ g(x) = x-(-2/3)`
We have to find the remainder when f(x) is divided by g(x).
By the remainder theorem, when f(x) is divided by g(x) the remainder is
`f(-2/3) =3 (-2/3)^4 + 2(-2/3)^3 - ((-2/3)^2) /3 - ((-2/3))/9 + 2/27`
` = 3 xx 16 /81 - 2 xx 8/27 - 4/27 + 2/27 + 2/27`
` = 16/27 - 16/27 - 4/27 + 2/27 + 2/27`
` = 0`
Remainder by actual division
Remainder is 0
APPEARS IN
संबंधित प्रश्न
If `f(x) = 2x^2 - 13x^2 + 17x + 12` find f(2)
In each of the following, using the remainder theorem, find the remainder when f(x) is divided by g(x) and verify the result by actual division: (1−8)
f(x) = x3 + 4x2 − 3x + 10, g(x) = x + 4
f(x) = 4x3 − 12x2 + 14x − 3, g(x) 2x − 1
Find the value of a such that (x − 4) is a factors of 5x3 − 7x2 − ax − 28.
3x3 − x2 − 3x + 1
x4 − 2x3 − 7x2 + 8x + 12
Write the remainder when the polynomialf(x) = x3 + x2 − 3x + 2 is divided by x + 1.
If f(x) = x4 − 2x3 + 3x2 − ax − b when divided by x − 1, the remainder is 6, then find the value of a + b
If x − 3 is a factor of x2 − ax − 15, then a =
Factorise the following:
(a + b)2 + 9(a + b) + 18
