Polynomials: Remainder and Factor Theorems — Engineering Board Exam Practice Questions

10 free engineering board exam reviewer questions on Polynomials: Remainder and Factor Theorems (Algebra), each with the correct answer and a worked solution.

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