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
Write the degrees of each of the following polynomials
`7x3 + 4x2 – 3x + 12`
Identify polynomials in the following:
`h(x)=x^4-x^(3/2)+x-1`
Identify constant, linear, quadratic and cubic polynomials from the following polynomials:
`q(x)=4x+3`
\[f(x) = 3 x^4 + 2 x^3 - \frac{x^2}{3} - \frac{x}{9} + \frac{2}{27}, g(x) = x + \frac{2}{3}\]
If the polynomials 2x3 + ax2 + 3x − 5 and x3 + x2 − 4x +a leave the same remainder when divided by x −2, find the value of a.
The polynomials ax3 + 3x2 − 3 and 2x3 − 5x + a when divided by (x − 4) leave the remainders R1 and R2 respectively. Find the values of the following case, if R1 + R2 = 0.
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
If x − 2 is a factor of the following two polynomials, find the values of a in each case x3 − 2ax2 + ax − 1.
If x2 + x + 1 is a factor of the polynomial 3x3 + 8x2 + 8x + 3 + 5k, then the value of k is
Factorise the following:
a4 – 3a2 + 2
