Advertisements
Advertisements
प्रश्न
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x + 1.
Advertisements
उत्तर
Let us denote the given polynomials as
`f(x) = x^3 + 3x^2 + 3x + 1,`
`g(x) = x + 1`
`⇒ g(x) = x-(-1),`
We will 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(-1)`
`= (-1)^3 + 3 (-1) + 1`
` = -1 + 3 -3 + 1`
`= 0`
APPEARS IN
संबंधित प्रश्न
Write the degrees of the following polynomials:
7
Find the integral roots of the polynomial f(x) = x3 + 6x2 + 11x + 6.
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x.
If x − 2 is a factor of the following two polynomials, find the values of a in each case x3 − 2ax2 + ax − 1.
3x3 − x2 − 3x + 1
x3 − 23x2 + 142x − 120
x3 − 2x2 − x + 2
x4 + 10x3 + 35x2 + 50x + 24
2x4 − 7x3 − 13x2 + 63x − 45
If x + 2a is a factor of x5 – 4a2x3 + 2x + 2a + 3, find a.
