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
Identify constant, linear, quadratic and cubic polynomials from the following polynomials:
`q(x)=4x+3`
f(x) = 2x4 − 6x3 + 2x2 − x + 2, g(x) = x + 2
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 x5 − 3x4 − ax3 + 3ax2 + 2ax + 4.
If both x + 1 and x − 1 are factors of ax3 + x2 − 2x + b, find the values of a and b.
2y3 + y2 − 2y − 1
2x4 − 7x3 − 13x2 + 63x − 45
If x − a is a factor of x3 −3x2a + 2a2x + b, then the value of b is
When x3 − 2x2 + ax − b is divided by x2 − 2x − 3, the remainder is x − 6. The values of a and b are respectively
(x + y)(x2 – xy + y2) is equal to
