Advertisements
Advertisements
Question
Find the remainder when x3 + 3x2 + 3x + 1 is divided by \[x - \frac{1}{2}\].
Advertisements
Solution
Let us denote the given polynomials as
`f(x) = x^3 + 3x^2 + 3x + 1,`
`h(x) = x-1/2`
We will find the remainder when f(x) is divided by h(x).
By the remainder theorem, when (f(x) is divided by h(x) the remainder is
`= f (1/2)`
` = (1/2)^3 + 3 (1/2)^2 + 3 (1/2) + 1`
`= 1/8 + 3/4 + 3/2 + 1`
`= 27 /8`
APPEARS IN
RELATED QUESTIONS
Identify constant, linear, quadratic and cubic polynomials from the following polynomials:
`h(x)=-3x+1/2`
f(x) = 2x4 − 6x3 + 2x2 − x + 2, g(x) = x + 2
f(x) = x3 − 6x2 + 2x − 4, g(x) = 1 − 2x
In each of the following, use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x) or, not: (1−7)
f(x) = x3 − 6x2 + 11x − 6; g(x) = x − 3
Show that (x − 2), (x + 3) and (x − 4) are factors of x3 − 3x2 − 10x + 24.
Find α and β, if x + 1 and x + 2 are factors of x3 + 3x2 − 2αx + β.
y3 − 2y2 − 29y − 42
If x140 + 2x151 + k is divisible by x + 1, then the value of k is
The value of k for which x − 1 is a factor of 4x3 + 3x2 − 4x + k, is
If (x − 1) is a factor of polynomial f(x) but not of g(x) , then it must be a factor of
