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

Use synthetic division to find the quotient when 2x3-3x2+5x-7 is divided by x-2.

  1. 2x2+x+7
  2. 2x2-x+7
  3. 2x2+x-7
  4. 2x2+7x+1

Answer

A. 2x2+x+7

Solution

With root 2: bring down 2; -3+2(2)=1; 5+1(2)=7; -7+7(2)=7. The quotient is 2x2+x+7 with remainder 7.

More Polynomials: Remainder and Factor Theorems questions

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

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