Topic 5

Solving Quadratic Equations by Factoring

100

3x²+25x+42

(3x+7)(x+6)

200

5x²+26x+24 

(5x+6)(x+4)

300

x²+9x+20

(x+4)(x+5)=x2+5x+4x+20=x2+9x+20

400

x²+7x+12

(x+3)(x+4)=x2+4x+3x+12=x2+7x+12

500

x²-7x-18

(x+2)(x−9)=x2−9x+2x−18=x2−7x−18

Quadratic Formula

100

15a²+18a+3=4a

a={-1/3,-3/5}

200

4r²+10r+1=6r

r={-1/2}

300

−2k²+11k+5=−4k²

k={-1/2,-5}

400

16c²-32c+9=−6

c={5/4,3/4}

500

8p²+6p−8=11

p={3/4,-3/2}

Square Root Property

100

x²-1=24

X=5

200

x²=36

x=6

Completing the Square

100

x²+2x−80=0

x={8,−10}

200

x²−18x=-80

x={8,10}

300

x²−16x+63=0

x={7,9}

400

x²+6x+8=0

x={−2,−4}

500

x²+6x−40=0

x={−10,4}

Factor by Grouping / Factor by GCF & Using a Pattern

100

2x³-5x²-4x+10

(x²−2)(2x−5)

200

2x³-5x²+2x-5

(x²+1)(2x−5)

300

Are Frogs Great?

YES

400

−28x⁴y³z³−21x⁶y⁶z⁴

−7x⁴y³z³(4+3x²y³z)

500

36x²y⁴z⁵+3xyz⁴

3xyz⁴(12xy³z+1)