Solving Polynomials Using Factoring Techniques

Trinomials (a=1,a>1)

100

What are the solutions to the following polynomial equation: 

x² + 10x + 24 = 0

=> (x+6)(x+4) = 0

=> x = -6,-4

200

What are the solutions to the following polynomial equation: 

x² -3x - 54 = 0

=> (x-9)(x+6) = 0

=> x = 9,-6

300

What are the solutions to the following polynomial equation: 

x² +2x - 63 = 0

=> (x+9)(x-7) = 0

=> x = -9,7

400

What are the solutions to the following polynomial equation: 

2x² +5x - 3 = 0

=> (2x-1)(x+3) = 0

=> x = 1/2, -3

500

What are the solutions to the following polynomial equation: 

3x² +8x +4 = 0

=> (3x+2)(x+2) = 0

=> x = -2/3, -2

GCF, Quadratic Pattern(Quartic Trinomial)

100

What are the solutions to the following polynomial equation: 

x³ + 5x² -14x = 0

=> x(x²+5x-14) = 0

=> x(x-2)(x+7) = 0

=> x =0, 2,-7

200

What are the solutions to the following polynomial equation: 

2x³ -10x² -12x = 0

=> 2x(x²-5x-6) = 0

=> 2x(x-6)(x+1) = 0

=> x =0, 6,-1

300

What are the solutions to the following polynomial equation: 

3x³ -33x² +30x = 0

=> 3x(x²-11x+10) = 0

=> 3x(x-1)(x-10) = 0

=> x =0, 1,10

400

What are the solutions to the following polynomial equation: 

x⁴ -11x² +30 = 0

=> (x²-6)(x²-5)=0

=> x²=6  x²=5

=> x =sqrt 6, -sqrt6, sqrt 5,-sqrt5

500

What are the solutions to the following polynomial equation: 

x⁴ -5x² -36 = 0

=> (x²-9)(x²+4)=0

=> x²=9  x²=-4

=> x =3, -3, 2i,-2i

Factoring by Grouping

100

What are the solutions to the following polynomial equation: 

x³ + x² -25x-25 = 0

=> (x²-25)(x+1)

=> x= 5,-5-1

200

What are the solutions to the following polynomial equation: 

x³ + 6x² -x -6 = 0

=> (x²-1)(x+6)

=> x= 1,-1,-6

300

What are the solutions to the following polynomial equation: 

x³ + 5x² -2x -10 = 0

=> (x²-2)(x+5)

=> x= sqrt2,-sqrt2,-5

400

What are the solutions to the following polynomial equation: 

2x³ -3x² -4x +6 = 0

=> (x²-2)(2x-3)

=> x= sqrt2,-sqrt2,3/2

500

What are the solutions to the following polynomial equation: 

x³ -5x² +4x -20 = 0

=> (x²+4)(x-5)

=> x= 2i,-2i,5

Write a Polynomial...

100

Write a polynomial of degree 2 in standard form (ax²+bx+c=0)

with the following roots:

2, 1

(x-2)(x-1)

x²-3x+2

200

Write a polynomial of degree 3 in factored form with the following roots:
0.-2,5

x(x + 2)(x - 5)

300

Write a polynomial of degree 4 in factored form with the following roots:
0.-2,sqrt5

x(x+2)(x-sqrt5)(x+sqrt5)

400

Write a polynomial of degree 4 in factored form with the following roots:
1,2,3i

(x-1)(x-2)(x-3i)(x+3i)

500

Write a polynomial of degree 3 in expanded form with the following roots:

2i, -1

(x-2i)(x+2i)(x+1)

(x²+4)(x+1)

=>x³+x²+4x+4

DOTS & Cubes

100

Factor (x²-81)

What is (x+9)(x-9)?

200

Factor x³-27

What is (x-3)(x²+3x+9)?

300

Factor 50x⁴-2x²

What is 2x²(5x+1)(5x-1)?

400

Factor 7n³-7

What is 7(n-1)(n²+n+1)?

500

Factor b²-(a-c)²

What is (b+a-c)(b-a+c)?