Advertisements
Advertisements
प्रश्न
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x.
उत्तर
Let us denote the given polynomials as
`f(x) = x^3 + 3x^2 + 3x + 1,`
`i(x) = x`
`⇒ i(x) = x-0,`
We will find the remainder when f(x) is divided by i(x).
By the remainder theorem, when f(x) is divided by i(x) the remainder is
` = f(0)`
` = (0)^3 + 3(0)^2 + 3 (0) + 1`
` = 0 + 0 + 0 +1`
` = 1`
APPEARS IN
संबंधित प्रश्न
Write the coefficient of x2 in the following:
`pi/6x^2- 3x+4`
Identify polynomials in the following:
`q(x)=2x^2-3x+4/x+2`
f(x) = 4x4 − 3x3 − 2x2 + x − 7, g(x) = x − 1
\[f(x) = 3 x^4 + 2 x^3 - \frac{x^2}{3} - \frac{x}{9} + \frac{2}{27}, g(x) = x + \frac{2}{3}\]
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x + 1.
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
Find the values of p and q so that x4 + px3 + 2x3 − 3x + q is divisible by (x2 − 1).
Find the values of a and b so that (x + 1) and (x − 1) are factors of x4 + ax3 − 3x2 + 2x + b.
y3 − 7y + 6
Factorise:
3x3 – x2 – 3x + 1
