Advertisements
Advertisements
Question
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x + π.
Advertisements
Solution 1
Let p(x) = x3 + 3x2 + 3x + 1
x + π = 0 ⇒ x = -π
∴ Remainder = (-π)3 + 3(-π)2 - 3(-π) + 1
= -π3 + 3π2 - 3π + 1
Therefore, the remainder is -π3 + 3π2 - 3π + 1.
Solution 2
By long division,
Therefore, the remainder is -π3 + 3π2 - 3π + 1.
RELATED QUESTIONS
Find 'a' if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
The polynomials 2x3 – 7x2 + ax – 6 and x3 – 8x2 + (2a + 1)x – 16 leaves the same remainder when divided by x – 2. Find the value of ‘a’.
When x3 + 3x2 – mx + 4 is divided by x – 2, the remainder is m + 3. Find the value of m.
Find without division, the remainder in the following:
5x3 - 7x2 +3 is divided by (x-1)
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x + `(1)/(2)`.
By remainder theorem, find the remainder when, p(x) is divided by g(x) where, p(x) = x3 – 3x2 + 4x + 50; g(x) = x – 3
If x51 + 51 is divided by x + 1, then the remainder is
Without actual division, prove that 2x4 – 5x3 + 2x2 – x + 2 is divisible by x2 – 3x + 2. [Hint: Factorise x2 – 3x + 2]
What must be subtracted from the polynomial x3 + x2 – 2x + 1, so that the result is exactly divisible by (x – 3)?
The remainder, when x3 – x2 + x – 1 is divided by x + 1, is ______.
