Multiply Polynomials and Factoring Polynomials (Algebra 1) QUESTIONS ONLY

Factoring GCF

100

The GCF of 30x⁴  and 25x²

Answer:  What is 

5x²

(GCF of 30x⁴  and 25x²) 

200

Factor:  

 12x³ + 16x²   

Answer:  What is

4x²(3x + 4)

Factor out the GCF

300

Factor: 

18x⁴ + 2x² - 6x  

Answer:  What is 

2x (9x³ + x - 3) 

Factor out the GCF

400

Factor:  

50x²y⁴- 40xy⁷

Answer:  What is 

10xy⁴ (5x - 4y³) 

Factor out the GCF

500

Factor completely: 

24x³-6x

Answer: What is  

6x(2x + 1) (2x - 1)  

GCF then DOTS

24x³ - 6x  =  6x(4x² - 1) 

= 6x(2x + 1) (2x - 1)  

Factoring DOTS(Difference of Two Squares)

100

Factor: 

x² - 36

Answer:  What is 

(x + 6)  (x - 6)  

Difference of Two Squares

x² - 36 =  (x + 6)  (x - 6)  

200

Factor:

4x² - 9

Answer:  What is

(2x + 3)  (2x - 3)

Difference of Two Squares

4x² - 9 = (2x + 3)  (2x - 3) 

300

Factor:

16x² - 49y²

Answer:  What is

(4x + 7y)  (4x - 7y)

Difference of Two Squares

16x² - 49y² = (4x + 7y)  (4x - 7y)  

400

Factor completely:

25x² - 100

Answer: What is  

25(x + 2)  (x - 2)  

GCF then Difference of Two Squares

25x² - 100  =  25(x² - 4) =

25(x + 2) (x - 2)  

500

Factor completely:  

x⁴ - 81

Answer:  What is 

(x² + 9)(x + 3) (x - 3) 

Difference of Two Squares... twice  (watch that the SUM cannot be factored) 

x⁴ - 81  =  (x²+9)(x²-9) = (x²+9)(x + 3) (x - 3)

Factoring Trinomials 1 (a=1)

100

Factor:

x² + 8x + 12

Answer:  What is 

(x + 6)  (x + 2)  

unFOIL  

(2 numbers whose product is 12 and sum is 8)

200

Factor: 

m² - 11m + 18

Answer:  What is 

(m - 9)  (m - 2)  

unFOIL  

(2 numbers whose product is 18 and sum is -11)

300

Factor: 

x² + 5x - 24

Answer:  What is 

(x + 8) (x - 3) 

unFOIL  

(2 numbers whose product is -24 and sum is 5)

400

Factor: 

y² - 6y - 7

Answer:  What is 

(y - 7)(y + 1)

unFOIL  

(2 numbers whose product is -7 and sum is -6)

500

Factor completely: 

2n³ - 10n² - 28n

Answer:    What is 

2n(n - 7) (n + 2)  

GCF then unFOIL :  2n (n² - 5n - 14) 

=2n(n-7)(n+2)

(2 numbers whose product is -14 and sum is -5)

Factoring Trinomials 2(a>1)

100

Factor:

2x² + 3x - 9

Answer:  What is 

(2x-3)(x+3) 

unFOIL (watch middle term!)

200

Factor:  

5n² + 19n + 12

Answer:  What is 

(5n + 4) (n + 3) 

unFOIL  (watch middle term!) 

300

Factor:  

6x² - 35x - 6 

Answer: What is 

(x - 6) (6x + 1)  

unFOIL (watch middle term!) 

400

Factor:  

8x² + 6x - 35  

Answer:  What is 

(2x+5) (4x-7)

unFOIL (watch middle term!)

500

Factor completely: 

24x⁴ - 10x³ - 56x²  

Answer:  What is 

2x² (3x+4) (4x-7)

GCF then unFOIL (watch middle term!)

2x² (12x² - 5x - 28) = 2x² (3x+4)(4x-7)

Multiplying Polynomials OR Factor by Grouping

100

Multiply:

(5x - 3)(2x - 7)

Answer:   What is 

10x² - 41x + 21

Double Distributive/FOIL Method  

200

Multiply: 

(2x - 5)²

Answer: What is 

4x² - 20x + 25

(2x- 5)²  = (2x- 5) (2x- 5)= 4x² - 20x + 25

FOIL / Double Distributive (write out the problem!)

300

Factor:  

6x³-15x²-14x+35

Answer:  What is 

 (2x-5) (3x²-7)   

Factor by Grouping 

6x³-15x²-14x+35 = 3x²(2x-5) - 7(2x-5) 

= (2x-5) (3x²-7)

400

Factor: 

56n³+8n²-63n-9

Answer:  What is 

(7n+1) (8n²-9)

Factor by Grouping 

56n³+8n²-63n-9 = 8n2(7n+1)-9(7n+1) 

= (7n+1) (8n²-9)

500

Factor completely: 

18x³-45x²-8x+20

Answer:  What is 

(2x-5)(3x+2)(3x-2)

Factor by Grouping... then DOTS 

18x³-45x²-8x+20 = 9x²(2x-5) - 4(2x-5)  

= (2x-5) (9x²-4) = (2x-5)(3x+2)(3x-2)