Toolbox TinkerTilewrights · polynomials and factoring

Picks the right tool every time: the general factoring strategy.

General Factoring Strategy

The general factoring strategy. In MathBound, the free Algebra I adventure game, Toolbox Tinker 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

Analyze by Term Count. Identify the correct factoring method (Difference of Squares,Trinomial methods,or Grouping) based on the number of terms.
Multi-Step Factoring. Factor completely by first extracting a GCF and then factoring the resulting binomial (Difference of Squares).
Recursive Factoring. Recognize when a resulting factor can be factored a second time (e.g.,yielding another difference of squares).
Identify Prime Polynomials. Determine when a polynomial cannot be factored further using integer coefficients.

Worked examples

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

Example 1 · Analyze by Term Count

After

taking

out

the

GCF

of

5 x y + 25 x + 30 y + 150,

which

method

finishes

the

factoring?

$Trinomial$ $factoring$
$Perfect$ $square$ $trinomial$
$Difference$ $of$ $squares$
$Factoring$ $by$ $grouping$

Show the worked steps

$Take$ $out$ $5 : 5 (x y + 5 x + 6 y + 30) .$
$What$ $is$ $left$ $has$ $4$ $terms,$ $so$ $use$ $Factoring$ $by$ $grouping .$

Answer: $Factoring$ $by$ $grouping$

Example 2 · Multi-Step Factoring

Factor

completely:

3 x^{3} - 48 x

$3 x (x - 4)^{2}$
$3 x (x + 4)^{2}$
$(x + 4) (x - 4)$
$3 x (x + 4) (x - 4)$

Show the worked steps

$" Completely "$ $means$ $keep$ $going$ $until$ $nothing$ $factors$ $further.$
$Take$ $out$ $the$ $GCF$ $3 x$ $first.$
$x^{2} - 16$ $is$ $(x)^{2} - (4)^{2} .$
$A$ $difference$ $of$ $squares$ $factors$ $as$ $a$ $sum$ $times$ $a$ $difference:$ $(x + 4) (x - 4) .$

Answer: $3 x (x + 4) (x - 4)$

Example 3 · Recursive Factoring

Factor

completely:

5 x^{4} - 80

$(x^{2} + 4) (x + 2) (x - 2)$
$5 (x^{2} + 4) (x + 2) (x - 2)$
$5 (x^{2} - 4) (x + 2) (x + 2)$
$5 (x + 2)^{2} (x - 2)^{2}$

Show the worked steps

$Take$ $out$ $the$ $GCF$ $5$ $first.$
$x^{4} - 16$ $is$ $a$ $difference$ $of$ $squares:$ $(x^{2} + 4) (x^{2} - 4) .$
$The$ $second$ $bracket$ $is$ $itself$ $a$ $difference$ $of$ $squares,$ $so$ $keep$ $going.$
$The$ $first$ $bracket,$ $a$ $SUM$ $of$ $squares,$ $does$ $not$ $factor$ $further.$

Answer: $5 (x^{2} + 4) (x + 2) (x - 2)$

Where it is in your textbook

Textbook	Lessons
Standard course	8.7
Big Ideas Math Algebra 1	7.8
Big Ideas Math Algebra 1 (2022)	7.8
CPM Core Connections Algebra	8.1.4
Glencoe Algebra 1	8-7, 8-8
Holt McDougal Larson Algebra 1	8.8
Math Nation Algebra 1 (Florida B.E.S.T.)	7.5, 7.8
OpenStax Elementary Algebra 2e	7.5
Pearson Algebra 1 Common Core	8-8
Reveal Algebra 1	10-7

Ready for Toolbox Tinker?

Play this battle free Play the whole adventure