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Polynomial Operations

A free Algebra II lesson from the “Polynomial Arithmetic” unit, with a worked example and practice problems including step-by-step solutions.

Polynomials are expressions made of terms with whole-number exponents. Add and subtract by combining like terms. Multiply using distribution and then combine like terms.

What you'll learn

Why it matters: Variable-side area sums, physics displacement totals, and stacked-fee budget rules all combine polynomial terms. Combining like terms collapses the expression into a single readable form so the next step is easier.

Worked example

Problem. Simplify (3x^2 + 5x - 2) + (x^2 - 7x + 9).

  1. Combine x^2 terms: 3x^2 + x^2 = 4x^2.
  2. Combine x terms: 5x - 7x = -2x.
  3. Combine constants: -2 + 9 = 7.

Answer: 4x^2 - 2x + 7

Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.

Practice problems

1. Simplify (2x + 5) + (3x - 8).

Show solution
  1. Combine like terms.

Answer: 5x - 3

2. Simplify (4x^2 - x) + (2x^2 + 7x).

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  1. Combine x^2 terms and x terms.

Answer: 6x^2 + 6x

3. Simplify (5x^2 + 3x - 1) - (2x^2 - x + 4).

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  1. Distribute the subtraction first.

Answer: 3x^2 + 4x - 5

4. Multiply (x + 4)(x + 5).

Choices: x^2 + 9x + 20 · x^2 + 20 · x^2 + x + 20 · 2x + 9

Show solution
  1. Use distribution.

Answer: x^2 + 9x + 20

5. The degree of 7x^4 - 3x^2 + 8 is...

Choices: 4 · 7 · 2 · 8

Show solution
  1. Degree is the highest exponent.

Answer: 4

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