Factoring and Solving Quadratics

Factor completely

100

Factor completely

x^2+3x

x(x+3)

200

Factor completely

125x^2-5

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

300

Factor completely

a^2+12a+32

(a+4)(a+8)

400

Factor completely

5n^2+10n-120

5(n+6)(n-4)

500

Factor completely

9x^2-27x-10

(3x-10)(3x+1)

Solve equations by factoring

100

Find the solutions/roots to the quadratic equation

v^2+3v-18=0

v= {-6,3}

200

Find the solutions/roots to the quadratic equation

r^2+r-56=0

r={-8,7}

300

Find the solutions/roots to the quadratic equation

p^2-9p=-18

p={3,6}

400

Find the solutions/roots to the quadratic equation 

7x^2+20x+12=0

{-6/7,-2}

500

Find the solutions/roots to the quadratic equation 

6m^2+53m+40=0

{-5/6,-8}

Solve by taking square roots

100

Solve by taking square roots

n^2=2

{sqrt2, -sqrt2}

200

Solve by taking square roots

k^2=-49

{7i,-7i}

300

Solve by taking square roots

2x^2=-100

{5isqrt2,-5isqrt2}

400

Solve by taking square roots

b^2+7=16

{3,-3}

500

Solve by taking square roots

7(x-3)^2=448

x= {11,-5}

Solve using quadratic formula

100

Solve using quadratic formula

6r^2-11r-10=0

{-2/3, 5/2}

200

Solve using quadratic formula

6n^2+5n+4=0

(-5+isqrt71)/12, (-5-isqrt71)/12

300

Solve using quadratic formula

2x^2+9x=95

{5,-19/2}

400

Solve using quadratic formula

5n^2+2n=11

{(-1+2sqrt14)/5,(-1-2sqrt14)/5}

500

Solve using quadratic formula

4m^2=7m+2

{2,-1/4}

Find the discriminant

100

Find the discriminant and tell how number and type of solutions.

10p^2+p+2=0

-79; two imaginary solutions

200

Find the discriminant and tell how number and type of solutions.

-5x^2-6x-1=0

16; two real rational solutions

300

Find the discriminant and tell how number and type of solutions.

-8b^2-8b=2

0; one real rational solution

400

Find the discriminant and tell how number and type of solutions.

x^2-4x+3

4; two real, rational solutions

500

Find the discriminant and tell how number and type of solutions.

-9x^2+10=3x

369; two real, irrational solutions