Mr. Kone Math Hub · Review sheet

Polynomial Operations

Unit 12: Polynomials, Modeling & Comparison · AI-A.APR.1, AI-A.SSE.1

Notes

Like terms only. 3x² and 5x² combine; 3x² and 5x do not. Subtracting a polynomial means distributing the minus to every term.

Vocabulary

• polynomial: A sum of terms of the form ax^n where n is a whole number.

Practice (no calculator unless marked)

1. The expression (5x² − x + 4) − 3(x² − x − 2) is equivalent to
   • A. 2x² − 2x + 2
   • B. 2x² + 2x + 10
   • C. 2x⁴ − 2x² + 2
   • D. 2x⁴ − 2x² + 10
2. The expression −2(x² − 2x + 1) + (3x² + 3x − 5) is equivalent to
   • A. x² + x − 4
   • B. x² − x − 7
   • C. x² + 7x − 4
   • D. x² + 7x − 7
3. Which expression is equivalent to (x − 5)(2x + 7) − (x + 5)?
   • A. 2x² − 2x − 30
   • B. 2x² − 2x − 40
   • C. 2x² − 4x − 30
   • D. 2x² − 4x − 40
4. Factor 20x³ − 45x completely.
5. What is the degree of the polynomial 2x − x² + 4x³?
   • A. 1
   • B. 2
   • C. 3
   • D. 4
6. The expression 9m² − 100 is equivalent to
   • A. (3m − 10)(3m + 10)
   • B. (3m − 10)(3m − 10)
   • C. (3m − 50)(3m + 50)
   • D. (3m − 50)(3m − 50)
7. The expression (5x² − x + 4) − 3(x² − x − 2) is equivalent to
   • A. 2x² − 2x + 2
   • B. 2x² + 2x + 10
   • C. 2x⁴ − 2x² + 2
   • D. 2x⁴ − 2x² + 10
8. The expression −2(x² − 2x + 1) + (3x² + 3x − 5) is equivalent to
   • A. x² + x − 4
   • B. x² − x − 7
   • C. x² + 7x − 4
   • D. x² + 7x − 7