Factoring Polynomials

GCF of Monomials

100

What is the GCF of the monomials (12x²) and (8x³)?

4x²

200

 Find the GCF of (15a³b) and (25a²b²).

5a²b

300

Determine the GCF of (30m⁴n²) and (45m²n³).

15m²n²

400

What is the GCF of (24x⁵y²) and (36x²y³)?

12x²y²

500

Calculate the GCF of (50p³q⁴) and (75p²q²r).

25p²q²

Factoring Polynomials

100

Factor the polynomial (2x² + 8x).

2x(x+4)

200

Factor (x² + 7x + 10).

(x+5)(x+2)

300

Factor (3x² - 12).

3(x - 2)(x + 2)

400

Factor (5x³ + 15x² - 20x).

5x(x + 4)(x - 1)

500

Factor the polynomial (x⁴ - 16) completely.

(x² - 4)(x² + 4) 

OR (x - 2)(x + 2)(x² + 4)

Factoring x² + bx + c

100

Factor (x² + 5x + 6).

(x + 2)(x + 3)

200

What are the factors of (x² - 3x - 10)

(x - 5)(x + 2)

300

Factor (x² + 4x + 4).

(x + 2)(x + 2)

400

Factor (x² - 8x + 15).

(x - 3)(x - 5)

500

Find the factors of (x² + 2x - 35).

(x + 7)(x - 5)

Factoring Perfect Squares

100

Factor (x² - 9).

(x - 3)(x + 3)

200

What are the factors of (4x² - 25)?

(2x - 5)(2x + 5)

300

Factor (49y² - 1).

(7y - 1)(7y + 1)

400

Factor (16a² - 64).

16(a-2)(a+2)

OR (4a-2)(4a+2)

500

Factor (x⁴ - 16).

(x² - 4)(x² + 4)

Choosing Factoring Method

100

What factoring method should you try first when all terms in a polynomial share a common factor?

factoring out the GCF

200

What method would you use to factor the polynomial (x² - 49)?

difference of squares

300

You are given (2x² + 10x). What factoring method is most efficient?

factoring out the GCF

400

What method should you use to factor (x² + 11x + 24)?

factoring a simple trinomial (creating two binomials)

500

How do you determine if a polynomial like (36x² - 100) can be factored using the difference of squares method?

check if both terms are perfect squares and there's a subtraction sign