Algebra 1 Adding, Subtracting and Multiplying Polynomials Test Solutions and Scoring (PDF)
This algebra 1 polynomial operations test answers for Algebra 1 covers adding, subtracting and multiplying polynomials (Common Core A-APR.A.1), with a free PDF to print.
Algebra 1 · Common Core State Standards: A-APR.A.1
Algebra 1 polynomial operations test answers: worked solutions
Question 1 – Name polynomials [2 pts]
\(4x^{4} – 7x + 1\) is a trinomial of degree 4. \(9x^{2}\) is a monomial of degree 2.
trinomial, 4; monomial, 2
Scoring: 1 point for each polynomial (name and degree both correct).
Question 2 – Add polynomials [2 pts]
Combine like terms: \((6 – 2)x^{2} + (-3 + 5)x + (2 – 7)\).
\(4x^{2} + 2x – 5\)
Scoring: 1 point for two correct terms; 1 point for the full answer.
Question 3 – Subtract polynomials [2 pts]
Distribute the negative: \(4x^{2} – x + 9 – x^{2} – 6x + 3\).
\(3x^{2} – 7x + 12\)
Scoring: 1 point for distributing the negative correctly; 1 point for the answer.
Question 4 – Monomial times polynomial [2 pts]
\(2x \cdot x^{2} = 2x^{3}\), \(2x \cdot (-4x) = -8x^{2}\), \(2x \cdot 3 = 6x\).
\(2x^{3} – 8x^{2} + 6x\)
Scoring: 1 point for two correct terms; 1 point for the full answer.
Question 5 – Binomial product [2 pts]
\(x^{2} – 2x + 5x – 10\).
\(x^{2} + 3x – 10\)
Scoring: 1 point for the four partial products; 1 point for combining like terms.
Question 6 – FOIL with coefficients [2 pts]
First \(6x^{2}\), Outer \(15x\), Inner \(-4x\), Last \(-10\).
\(6x^{2} + 11x – 10\)
Scoring: 1 point for the partial products; 1 point for the final polynomial.
Question 7 – Special products [3 pts]
a) \(x^{2} + 18x + 81\).
b) \(x^{2} – 36\).
c) Squaring means multiplying the binomial by itself. The products \(9x\) and \(9x\) produce the middle term \(18x\).
\(x^{2} + 18x + 81\); \(x^{2} – 36\)
Scoring: 1 point per part.
Question 8 – Rectangle area [3 pts]
a) \((x + 7)(x + 2) = x^{2} + 2x + 7x + 14 = x^{2} + 9x + 14\).
b) \(9 + 27 + 14 = 50\), and also \((10)(5) = 50\).
\(x^{2} + 9x + 14\); 50
Scoring: part a, 1 point for the partial products and 1 point for combining; part b, 1 point.
Question 9 – Closure [2 pts]
Add: \(5x^{2}\), a polynomial.
It illustrates that polynomials are closed under addition: the sum of two polynomials is always a polynomial.
\(5x^{2}\)
Scoring: 1 point for the sum; 1 point for the closure statement.
Total score
20 points
Key facts behind this algebra 1 polynomial operations test answers
- The degree of a polynomial is its greatest exponent.
- Add or subtract by combining like terms; subtracting changes the sign of every term.
- Multiply by distributing each term, then combine like terms.
- (a + b)² = a² + 2ab + b² and (a + b)(a – b) = a² – b².
- The sum, difference, and product of polynomials is a polynomial.
How to use this algebra 1 polynomial operations test answers
Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.
All Algebra 1 chapters: Algebra 1 math.
Print this page
Download PDFDownload the Algebra 1 Adding, Subtracting and Multiplying Polynomials Test Solutions and Scoring (PDF, 92 KB)More Algebra 1 math
Lessons
See all
Worksheets
See all
Tests
See all
Exponent Rules and Radicals Test with Point Values- Linear Inequalities in Two Variables and Systems Test with Point Values
- Linear Inequalities in One Variable Test with Point Values
- Writing Linear Equations and Functions Test with Point Values
- Data Distributions and Summary Statistics Test with Point Values
- Arithmetic and Geometric Sequences Test with Point Values
