Magnet MaxTilewrights · polynomials and factoring

Pulls the shared piece out of everything: the greatest common factor and grouping.

Greatest Common Factor and Grouping

The greatest common factor and grouping. In MathBound, the free Algebra I adventure game, Magnet Max asks these problems, and the only way past is to solve them.

Part of Polynomials and Factoring: chapter 8 of the standard course.

Play this battle free

10 questions, no sign-up, nothing saved. Climbs from the basics to harder questions.

What you will practice

Find the GCF. Find the greatest common factor of two or more integer constants.
Factor the GCF. Factor a constant GCF from a polynomial using the reverse distributive property.
Factor by Grouping. Factor a four-term polynomial by grouping when the third term is positive.

Worked examples

Made by the game’s own question engine. Try each one, then open its steps.

Example 1 · Find the GCF

Find

the

GCF

of

42

and

98 .

$14$
$42$
$294$
$140$

Show the worked steps

$42 = 14 \cdot 3$ $and$ $98 = 14 \cdot 7 .$
$3$ $and$ $7$ $share$ $no$ $factor,$ $so$ $the$ $GCF$ $is$ $14 .$

Answer: $14$

Example 2 · Factor the GCF

Factor:

15 x - 10

$5 (15 x - 2)$
$15 (x - 2)$
$5 (3 x - 10)$
$5 (3 x - 2)$

Show the worked steps

$The$ $GCF$ $of$ $15$ $and$ $10$ $is$ $5 .$
$Dividing$ $each$ $term$ $by$ $5$ $leaves$ $(3 x - 2) .$

Answer: $5 (3 x - 2)$

Example 3 · Factor by Grouping

Factor:

5 x y + 25 x + 6 y + 30

$(5 x + 6) (y - 5)$
$(5 x - 6) (y + 5)$
$(5 x + 6) (y + 5)$
$(5 x + 5) (y + 6)$

Show the worked steps

$Group:$ $(5 x y + 25 x) + (6 y + 30) .$
$That$ $is$ $5 x (y + 5) + 6 (y + 5),$ $so$ $the$ $answer$ $is$ $(5 x + 6) (y + 5) .$

Answer: $(5 x + 6) (y + 5)$

Where it is in your textbook

Textbook	Lessons
Standard course	8.4
Big Ideas Math Algebra 1	7.4, 7.8
Big Ideas Math Algebra 1 (2022)	7.4, 7.8
CPM Core Connections Algebra	8.1.1
enVision Algebra 1	7-4, 7-6
enVision Algebra 1 (2024)	7-4, 7-6
Eureka Math Algebra I (EngageNY)	4.1-4.2, 4.3-4.4
Glencoe Algebra 1	8-5
HMH Into Algebra 1	17.4
Holt McDougal Larson Algebra 1	8.4, 8.8
Math Nation Algebra 1 (Florida B.E.S.T.)	7.1, 7.6
Open Up NC Math 1 (MVP)	7.3
OpenStax Elementary Algebra 2e	7.1
Pearson Algebra 1 Common Core	8-2, 8-8
Reveal Algebra 1	10-5
SpringBoard Algebra 1	26

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