This algebra 1 polynomials worksheet gives 23 problems on adding, subtracting and multiplying polynomials, ordered from easy to hard, with a separate answer key.
These 23 problems practice naming and writing polynomials, adding and subtracting them, and multiplying with the distributive property, FOIL, the box method and the special products (Common Core A-APR.A.1 and A-SSE.A.2).
The problems start with degree and standard form and get harder. The last six are word problems with areas, profit and mental math.
Algebra 1 Polynomials Worksheet: problems 1–5
Problem 1: Degree and terms
For \(4 x^{3} – 7 x + 2\), state the degree, the leading coefficient and the number of terms. Then classify it as a monomial, binomial or trinomial.
Problem 2: Standard form
Write \(5-2x^{2}+6x+x^{3}\) in standard form.
Problem 3: Classify polynomials
Name each polynomial by its number of terms and its degree.
- \(7x^{2}\)
- \(x^{2}-9\)
- \(2x^{3}+x-1\)
Problem 4: Add polynomials
Add \((3x^{2}+5x-4)+(2x^{2}-8x+9)\).
Problem 5: Subtract polynomials
Subtract \((7x^{2}-3x+1)-(4x^{2}+2x-6)\).
Algebra 1 Polynomials Worksheet: problems 6–10
Problem 6: Two variables
Add \((x^{2}+4xy-3y^{2})+(5x^{2}-2xy+y^{2})\).
Problem 7: Subtract with a missing term
Subtract \((6a^{3}-2a+5)-(a^{3}+4a^{2}-2a-3)\) and write the answer in standard form.
Problem 8: Multiply monomials
Multiply \((3x^{2})(-4x^{5})\).
Problem 9: Distribute a monomial
Multiply \(5x(2x^{2}-3x+4)\).
Problem 10: Box method
Use the area model to multiply \((x+4)(x+3)\).
Algebra 1 Polynomials Worksheet: problems 11–15
Problem 11: FOIL with a negative
Multiply \((2x-5)(x+6)\).
Problem 12: FOIL, both negative
Multiply \((3x-2)(4x-7)\).
Problem 13: Square of a binomial
Expand \((x+7)^{2}\). The figure shows a square with side \(x+7\).
Problem 14: Square of a difference
Expand \((3x-5)^{2}\).
Problem 15: Difference of squares
Multiply \((2x+9)(2x-9)\).
Algebra 1 Polynomials Worksheet: problems 16–20
Problem 16: Binomial times trinomial
Multiply \((x-3)(x^{2}+2x-5)\).
Problem 17: Closure
Add \((4x^{2}+3x)+(-4x^{2}+5)\). State the degree of the sum and explain whether the result is still a polynomial.
Problem 18: Garden area
Maya plans a rectangular garden that is \(x+8\) feet long and \(x+5\) feet wide. Write a polynomial for its area, then find the area when \(x=4\).
Problem 19: Profit polynomial
The school store sells \(x\) dozen cookies. Revenue is \(R=-x^{2}+50x\) dollars and cost is \(C=10x+120\) dollars. Write a polynomial for the profit \(P=R-C\), then find the profit for 10 dozen cookies.
Problem 20: Picture frame
Jamal puts a square photo with side \(x+2\) inches into a square frame with outer side \(x+8\) inches. Write a simplified polynomial for the area of the frame itself (the border), then find it when \(x=4\).
Algebra 1 Polynomials Worksheet: problems 21–23
Problem 21: Mental math
Priya calculates \(52\times 48\) in her head by writing it as a product of a sum and a difference. Show her steps and find the product.
Problem 22: Metal sheet with a cutout
A metal sheet is \(3x+4\) inches long and \(x+2\) inches wide. A square with side \(x\) inches is cut from one corner. Write a simplified polynomial for the area that remains, then evaluate it for \(x=3\).
Problem 23: Find the error
Noah writes \((x+5)^{2}=x^{2}+25\). Test his answer with \(x=1\), explain his mistake and write the correct expansion.
How to use this algebra 1 polynomials worksheet
Print this algebra 1 polynomials worksheet as a PDF, solve every problem on paper, then compare with the answer key.
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Algebra 1 Adding, Subtracting and Multiplying Polynomials worksheet
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