Advertisements
Advertisements
Question
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x + 1.
Advertisements
Solution
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
RELATED QUESTIONS
f(x) = x4 − 3x2 + 4, g(x) = x − 2
In the following two polynomials, find the value of a, if x − a is factor (x5 − a2x3 + 2x + a + 1).
In the following two polynomials, find the value of a, if x + a is a factor x4 − a2x2 + 3x −a.
What must be subtracted from x3 − 6x2 − 15x + 80 so that the result is exactly divisible by x2 + x − 12?
Factorize of the following polynomials:
4x3 + 20x2 + 33x + 18 given that 2x + 3 is a factor.
Find the remainder when x3 + 4x2 + 4x − 3 is divided by x.
Factorise the following:
12x2 + 36x2y + 27y2x2
(a + b – c)2 is equal to __________
Factorise:
2x3 – 3x2 – 17x + 30
Factorise:
x3 + x2 – 4x – 4
