Polynomials practice
Factor ten four-term cubics completely over the integers. Choose displayed monic, nonmonic or mixed leading coefficients and factorable-only practice or a set with three primitive prime cubics.
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
Factor each cubic completely over the integers by grouping the first two and last two terms. Write Prime over the integers when appropriate.
Download the practice pages alone, or include a separate answer key or teacher model. Longer activities may use more than one page.
Customize this worksheetGroup the first two terms and the last two terms. Extract each pair’s greatest common factor so the same binomial appears, then factor that shared binomial from the two groups.
Continue factoring after grouping. A difference of squares such as x² − 1 becomes two linear factors, while an irreducible quadratic stays as a factor of an otherwise factorable cubic.
Learning objective
Use a shared binomial from adjacent term pairs, then complete every remaining integer factorization.
Worked example
6(x − 1)(x + 1)(3x − 2).
Group to get 6[x²(3x − 2) − (3x − 2)] = 6(x² − 1)(3x − 2), then split x² − 1 into (x − 1)(x + 1).
Teaching notes
Make it yours
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.
A useful next step
Polynomials
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.
Preview and download
Polynomials
Divide polynomials by monic linear divisors in ten expression problems or six long-division problems. Choose binomial, trinomial, four-term or mixed dividends and check exact quotient-and-remainder keys.
Preview and download
