Question

Find the remainder when x³+3x²+3x+1 is divided by x+π.

A) 4π^3 + 3π^2 + 3π + 1
B) π^3 + 3π^2 + 3π + 1
C) 1
D) None of the above.

Answer 1

To find the remainder when dividing x³+3x²+3x+1 by x+π, use polynomial long division or synthetic division to divide the polynomial and find the remainder, which is 4π³+3π²+3π+1.

Step-by-step explanation:

To find the remainder when dividing x³+3x²+3x+1 by x+π, we can use the Remainder Theorem.

The Remainder Theorem states that if we divide a polynomial by a linear divisor, the remainder is equal to the polynomial evaluated at the negation of the divisor.

In this case, the divisor is x+π, so the negation is -(x+π).

Plugging this into the polynomial, we get:

R(x) = (x³+3x²+3x+1)|-(x+π)

Using polynomial long division or synthetic division, we can divide the polynomial to find the remainder:

R(x) = 4π³+3π²+3π+1