REVIEW ON FACTORING

Factoring trinomials when a=1

100

Factor into two binomials: x²-12x+27

(x-9)(x-3)

200

Factor into two binomials: x²+2x-24

(x+6)(x-4)

300

Factor into two binomials: x²-5x+6

(x-3)(x-2)

400

Factor into two binomials: x²+10x+25

(x+5)²

500

Factor into two binomials: y⁴-7y²-18

(y²-9)(y²-2)

Factoring trinomials when a>1

100

Factor 2x²-7x+6

(2x-3)(x-2)

200

Factor 9x²+6x+1

(3x+1)²

300

Factor 2x²-x-6

(x-2)(2x+3)

400

Factor 4y²+12y+9

(2y+3)²

500

Factor: ax²-bx-ax+b

(x-1)(ax-b)

Factoring the difference of two perfect squares

100

Factor: x²-16

(x+4)(x-4)

200

Factor: 9-x²

(3+x)(3-x)

300

25y²-4k²

(5y+2k)(5y-2k)

400

1/4x²-(49/25)

(1/2x-7/5)(1/2x+7/5)

500

x²+100

Cannot be factored because of the plus sign.

Factor completely

100

Factor completely: a²b²-144a²

a²(b+12)(b-12)

200

Factor completely: 2x³+14x²-60x

2x(x+10)(x-3)

300

Factor completely: y²-81

(y²+9)(y+3)(y-3)

400

Factor completely: x⁴-625

(x+5)²(x²+25)

500

Factor completely: 80-5d²

5(4+d)(4-d)

Factoring with trig. functions

100

Factor: sin²x - 1

(sinx - 1)(sinx + 1)

200

Factor: tan²x - 5tanx + 6

(tanx -2)(tanx - 3)

300

Factor: cos²x + 2cosx + 1

(cosx + 1)²

400

Factor: 4csc²x+12cscx+9

(2cscx+3)²

500

Factor out completely: 12sec⁴x + 33sec²x - 135

3(sec²x + 5)(2secx - 3)(2secx + 3)