Factoring

GCF

100

The greatest common factor between 16 and 48

What is 16?

200

The greatest common factor between 20x³ and 15x⁴

What is 5x³?

300

The greatest common factor between 13x³, 22x², and 26x

What is x?

400

True or false: if the coefficient of one of the terms is prime (only divisible by 1 and itself), and the terms do not share a common variable, the GCF will be 1.

What is False?

500

The number of times we factor out the GCF - or attempt to - in a standard trinomial factoring problem (ax² + bx +c)

What is 3?

600

The GCF of 3x² and 0x

What is 3x²?

Factor

100

Factor completely: 3x+9

What is 3(x+3)?

200

Factor completely: 6x² + 4x

What is 2x(3x+2)?

300

The operation that we undo when factoring.

Bonus 100: the operation we perform when factoring

What is distribution?

Bonus: What is division?

400

Factor completely: 2x² -7x - 30

What is (x-6)(2x+5)?

500

Factor completely: 5x² + 60x + 25 (250)

True or False: This polynomial is prime (250)

What is 5(x² + 12x +5)?

What is False?

600

True or False: -12x² + 27 is a prime polynomial.

If false, factor completely.

What is False; -3(2x+3)(2x-3)?

Special Cases

100

Factor completely: x² - 81

What is (x+9)(x-9)?

200

Factor completely: 

28x² - 63

What is 7(2x+3)(2x-3)?

300

Factor completely: x² + 22x + 121

What is (x+11)²?

400

True or False: -12x² + 27 is a prime polynomial.

If false, factor completely.

What is False; -3(2x+3)(2x-3)?

500

Factor completely: 12x² + 288x + 1728

Hint: 1728 = 12³

What is 12(x+12)²?

600

Factor completely: 2x⁵ - 1250x

What is 2x(x-5)(x+5)(x²+25)?

Multi variable

100

The GCF of xy² and y³z

What is y²?

200

The GCF of 4x²y⁴ and 6x³y

What is 2x²y?

300

The GCF of 6x²z³, 12x²yz, and 7y³?

What is 1?

400

Factor completely: -14xy² - 7x² + 21x²y³

What is -7x(2y² + x - 3xy³)?

500

Factor completely: a² +2ab + b²

What is (a+b)²?

600

**DOUBLE POINTS**

Work through this problem as a team.

Factor completely: 6x²y²z² + 3xyz⁵ + 24xy⁵z + 12y⁴z⁴

Hint: Think of this like ax² + bx + c; what would b split into, and how could we group?

What is 3yz(xz + 4y³)(2xy+z³)?

Theory

100

Definition of GCF (more than greatest common factor)

What is the biggest number that evenly divides each term listed?

200

The step after we group when factoring a trinomial

What is GCF factoring?

300

The name for the following property:

a² - b² = (a+b)(a-b)

What is the Difference of Two Squares?

400

For a trinomial ax² + bx + c, the reason why we multiply a and c (think what step of binomial multiplication we undo)

What is to undo combining like terms?

500

Student A factors out a 6 at the start of a problem and ends with the solution:

6(x+7)(3x-9)

True or false: Student A did not factor out the GCF in the first step. (300) Explain how you know. (200)

What is True?

Because there is still a factor of 3 that can be pulled out from the last binomial.

600

The reason why GCF does not work well as a descriptor when factoring out a variable term

What is the idea that x can be negative or a fraction, and factoring out that value of x could lower our value?