Engineering Board Exam Reviewer · Polynomials: Remainder and Factor Theorems · easy

Find the remainder when x3-2x2+4x-5 is divided by x-2.

1. 3
2. -5
3. 11
4. 7

Answer

A. 3

Solution

By the remainder theorem, the remainder is f(2)=8-8+8-5=3.

More Polynomials: Remainder and Factor Theorems questions

1. The roots of x3-6x2+kx-6=0 are in arithmetic progression. Find k.
2. Find the remainder when 2x101+3x100-5 is divided by x+1.
3. If x-1 and x+2 are both factors of x3+px2+qx-6, find pq.
4. Find the monic polynomial of lowest degree whose roots are 1, -2, and 3.
5. Find the sum of the roots of 2x3-5x2+3x-8=0.
6. Use synthetic division to find the quotient when 2x3-3x2+5x-7 is divided by x-2.
7. When x3+ax+7 is divided by x+2 the remainder is -3. Find a.
8. Find all roots of x3-3x2-4x+12=0.
9. Find k so that x-2 is a factor of x2+kx-10.

All Polynomials: Remainder and Factor Theorems questions