FACTORING POLYNOMIALS

Factoring trinomials

100

Factor completely: x²+8x+12

(x+6)(x+2)

200

Factor completely:     

m²-11m+18

(m-9)(m-2)

300

Factor completely: x²+5x-24

(x+8)(x-3)

400

Factor completely:      

 y²-6y-7

(y-7)(y+1)

500

Factor completely:     x²-x-56

(x-8)(x+7)

Factoring Trinomials- harder

100

Factor completely: 2x²+7x+3

(2x+1)(x+3)

200

Factor completely: 5n²+26n+5

(5n+1)(n+5)

300

Factor completely:    

3x²-10x+7

(3x-7)(x-1)

400

Factor completely:    

7x²-36x+5

(7x-1)(x-5)

500

Factor completely:    

2x²-12x+10

2(x-1)(x-5)

Factoring by Difference of 2 Squares

100

Factor completely:     

4x²-9

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

200

Factor completely: 81x²-1

(9x+1)(9x-1)

300

Factor completely:      4x²-16

(2x+4)(2x-4)

400

Factor completely: 25x²+30x+9

(5x+3)(5x+3)

500

Factor completely:     

9x²-16y²

(3x+4y)(3x-4y)

Factor by GCF

100

Factor completely: 14n²+10n

2n(7n+5)

200

Factor completely: 18x³-6x

6x(3x²-1)

300

Factor completely: 

20m²+5m-15

5(4m-3)(m+1)

400

Factor completely: 

mx²-18mx+81m

m(x-9)²

500

Factor completely:   

26y-6y²-8

2(y-4)(-3y+1)

Applications

100

The shorter side of a rectangle is 3 less than the longer side. The area is 54. Find the length and width.

9 units by 6 units

200

When 10 is subtracted from the square of a number the result is three times the number. What is the positive solution?

5

300

The difference of the squares of two consecutive even integers is 68. What are these numbers?

16,18

400

Find three consecutive positve odd integers such that the product of the first and third is one more than four times the second.

3, 5, 7 

500

A rectangular garden is surrounded by a walk of uniform width. The area of the garden is 180 square yards. If the dimensions of the garden plus the walk are 16 yards by 24 yards, find the dimensions of the garden.

18 ft by 10 ft