Advertisements
Advertisements
प्रश्न
Find the remainder when x3 + 3x2 + 3x + 1 is divided by \[x + \pi\] .
Advertisements
उत्तर
Let us denote the given polynomials as
`f(x) = x^3 + 3x^2 + 3x + 1`
`j(x) = x+pi`
`⇒ j (x) = x-(-pi),`
We will find the remainder when f(x) is divided by j(x) .
By the remainder theorem, when f(x) is divided by j(x)the remainder is
` = f(- pi)`
`= (- pi) ^3 + 3(-pi)^2 +3(- pi)+1`
` = -pi^3 + 3pi^2 -3pi +1`
APPEARS IN
संबंधित प्रश्न
Write the degrees of each of the following polynomials
`7x3 + 4x2 – 3x + 12`
Write the degrees of the following polynomials:
7
If `f(x) = 2x^2 - 13x^2 + 17x + 12` find f(2)
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
Find the value of a, if x + 2 is a factor of 4x4 + 2x3 − 3x2 + 8x + 5a.
Find α and β, if x + 1 and x + 2 are factors of x3 + 3x2 − 2αx + β.
If x + 2a is a factor of x5 – 4a2x3 + 2x + 2a + 3, find a.
Factorise:
x3 + x2 – 4x – 4
