Solving Polynomials Review

Solving Polynomials by Factoring Pt 1(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

Solving Polynomials by Factoring Pt 2 (GCF, 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

Solving Polynomials by Factoring Pt 3(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

Dividing Polynomials

100

Find the remainder: 347 ÷ 16

11

200

Find the quotient: (x² + 10x + 21) ÷ (x + 3)

x + 7

300

Find the quotient and remainder: (2x² + 7x + 8) ÷ (x + 2)

Quotient: 2x + 3, remainder: 2

400

Find the quotient and remainder: (x³ + 3x² - x + 2) ÷ (x - 1)

Quotient: x² + 4x + 3, remainder: 5

500

Find the quotient and remainder: (x³ + 11x + 12) ÷ (x + 3)

Quotient: x² - 3x + 20, remainder: -48

Simplify Square Roots

100

What is the square root of -1?

i

200

sqrt(-8)

+2i sqrt(2), -2i sqrt(2)

300

sqrt(-200)

10i sqrt(2), -10i sqrt(2)

400

sqrt(-324)

18i, -18i

500

sqrt(-252)

-6i sqrt(7), 6i sqrt(7)