Kuta Software-Infinite Algebra 1 - Factoring By Grouping - Factor each completely

Oct 8, 2026

Uploaded by Ivy

Worksheet for Infinite Algebra 1 practice focused on factoring polynomials by grouping. Includes multiple problems labeled 1 through 28, each requiring complete factorization of algebraic expressions with variables and coefficients in different forms. A key section provides the factored results for each item, supporting self-check and step-by-step study for mastering grouping-based factoring techniques.

LanguageEnglish

CategoryExam

FormatPDF

Pages4

Reading Time10 min

AccessFree to download

Factoring By Grouping

Factor each completely

Answers and factored forms

Kuta Software-Infinite Algebra 1 Name___________________________________ Factoring By Grouping Date________________ Period____ Factor each completely. 1) 8r3 − 64r2 + r − 8 2) 12 p3 − 21 p2 + 28 p − 49 3) 12x3 + 2x2 − 30x − 5 4) 6v3 − 16v2 + 21v − 56 5) 63n3 + 54n2 − 105n − 90 6) 21k3 − 84k2 + 15k − 60 7) 25v3 + 5v2 + 30v + 6 8) 105n3 + 175n2 − 75n − 125 9) 96n3 − 84n2 + 112n − 98 10) 28v3 + 16v2 − 21v − 12 11) 4v3 − 12v2 − 5v + 15 12) 49x3 − 35x2 + 56x − 40 13) 24 p3 + 15 p2 − 56 p − 35 14) 24r3 − 64r2 − 21r + 56 15) 56xw + 49xk2 − 24 yw − 21 yk2 16) 42mc + 36md − 7n2 c − 6n2 d 17) 12x2 u + 3x2 v + 28 yu + 7 yv 18) 40ac2 + 25ak2 + 32bc2 + 20bk2 19) 12bc − 4bd − 15xc + 5xd 20) 16mn − 4m2 + 28n − 7m 21) 56xy − 35x + 16ry − 10r 22) 21xy + 15x + 35ry + 25r 23) 5a2 z − 4a2 c + 15xz − 12xc 24) 4xy + 6 − x − 24 y 25) 21xy − 12b2 + 14xb − 18by 26) 9mz − 4nc + 3mc − 12nz 27) 28xy + 25 + 35x + 20 y 28) 30uv + 30u + 36u2 + 25v Kuta Software-Infinite Algebra 1 Factoring By Grouping Factor each completely. 1) 8r3 − 64r2 + r − 8 (8r2 + 1)(r − 8) Name___________________________________ Date________________ Period____ 2) 12 p3 − 21 p2 + 28 p − 49 (3 p2 + 7)(4 p − 7) 3) 12x3 + 2x2 − 30x − 5 4) 6v3 − 16v2 + 21v − 56 (2x2 − 5)(6x + 1) (2v2 + 7)(3v − 8) 5) 63n3 + 54n2 − 105n − 90 6) 21k3 − 84k2 + 15k − 60 3(3n2 − 5)(7n + 6) 3(7k2 + 5)(k − 4) 7) 25v3 + 5v2 + 30v + 6 8) 105n3 + 175n2 − 75n − 125 (5v2 + 6)(5v + 1) 5(7n2 − 5)(3n + 5) 9) 96n3 − 84n2 + 112n − 98 10) 28v3 + 16v2 − 21v − 12 2(6n2 + 7)(8n − 7) (4v2 − 3)(7v + 4) 11) 4v3 − 12v2 − 5v + 15 12) 49x3 − 35x2 + 56x − 40 (4v2 − 5)(v − 3) (7x2 + 8)(7x − 5) 13) 24 p3 + 15 p2 − 56 p − 35 14) 24r3 − 64r2 − 21r + 56 (3 p2 − 7)(8 p + 5) (8r2 − 7)(3r − 8) 15) 56xw + 49xk2 − 24 yw − 21 yk2 16) 42mc + 36md − 7n2 c − 6n2 d (7x − 3 y)(8w + 7k2 ) (6m − n2 )(7c + 6d) 17) 12x2 u + 3x2 v + 28 yu + 7 yv 18) 40ac2 + 25ak2 + 32bc2 + 20bk2 (3x2 + 7 y)(4u + v) (5a + 4b)(8c2 + 5k2 ) 19) 12bc − 4bd − 15xc + 5xd 20) 16mn − 4m2 + 28n − 7m (4b − 5x)(3c − d) (4m + 7)(4n − m) 21) 56xy − 35x + 16ry − 10r 22) 21xy + 15x + 35ry + 25r (7x + 2r)(8 y − 5) (3x + 5r)(7 y + 5) 23) 5a2 z − 4a2 c + 15xz − 12xc 24) 4xy + 6 − x − 24 y (a2 + 3x)(5z − 4c) (x − 6)(4 y − 1) 25) 21xy − 12b2 + 14xb − 18by 26) 9mz − 4nc + 3mc − 12nz (7x − 6b)(3 y + 2b) (3m − 4n)(3z + c) 27) 28xy + 25 + 35x + 20 y 28) 30uv + 30u + 36u2 + 25v (7x + 5)(4 y + 5) (6u + 5)(5v + 6u) Create your own worksheets like this one with Infinite Algebra 1. Free trial available [at KutaSoftware.com](at KutaSoftware.com)

FAQs

What skill does this worksheet practice?

It practices factoring polynomials completely using the method of grouping.

How are the problems presented?

The worksheet lists many expressions numbered 1 through 28, instructing you to factor each one completely.

Does the document include solutions?

Yes. After each set of problems, it shows the factored forms for checking your work.

Oct 8, 2026

Uploaded by Ivy