Polynomials
Multiplying binomials worksheets
Expand ten products of two binomials. Choose among four expression structures, form every term pair and collect like terms with a separate worked key.
Preview and downloadPolynomials practice
Factoring quadratic polynomials worksheets
Factor ten quadratic binomials and trinomials completely over the integers. Choose factorable-only practice or include two prime quadratics, and vary monic and nonmonic leading coefficients.
Ready-made English PDF · fixed settings
Customization below makes a separate PDF.
Fixed English ready-made files. Custom settings below apply only to the configured PDF.
Ready to print
Start with a ready-made worksheet
Factor each polynomial completely over the integers. Write Prime over the integers when the polynomial cannot be factored further.
Download the practice pages alone, or include a separate answer key or teacher model. Longer activities may use more than one page.
Customize this worksheetFactor completely over the integers
Begin with any numerical or variable greatest common factor. Then factor the primitive quadratic into linear factors when possible. A primitive quadratic with a negative or non-square discriminant is prime over the integers.
Multiply the complete product to check its leading, middle and constant coefficients against the original expression.
Learning objective
What this activity builds
Extract every common factor and factor the remaining quadratic completely over the integers.
Worked example
Factor 6x² + 14x − 40 completely.
2(3x − 5)(x + 4).
First extract the content 2. The primitive quadratic 3x² + 7x − 20 factors as (3x − 5)(x + 4), and the complete product expands to the original polynomial.
Teaching notes
Make the practice count
- Extract a numerical or variable greatest common factor before factoring the primitive quadratic.
- Use the product ac and the middle coefficient b to organize a nonmonic trinomial.
- Check every answer by multiplying the complete product back to the displayed polynomial.
- A primitive quadratic is prime over the integers when its discriminant is negative or not a perfect square.
Make it yours
Customize the practice
Choose your options, update the preview, then download the exact same pages.
Choose the expression structures to practice. Answer editions show the steps for each problem.
Enlarged pages scroll. PDF size stays the same.
A useful next step
Related activities
Polynomials
Factoring monomials worksheets
Factor ten monomials into primes and variable factors. Choose expression structures, coefficient ranges and repeated factors or prime-power notation, with exact worked answers.
Preview and download