Polynomials and Polynomial Functions

Operations with Complex Numbers

100

Add the complex numbers: (2 + 10i)+(7 - 15i)

9 - 5i

200

Multiply the complex numbers: (3 - 2i)(3 + 4i)

17 + 6i

300

Subtract the complex numbers: (6 + 5i) - (1 - 8i)

5 + 13i

400

Simplify and write in the standard form of a complex number. 

(-20 + √-50)/-10

 

2 - √2i/2

500

Divide: 

(-3 + 5i)/(-3 + i)

7/5 - 6/5i

Graphs of Polynomials

100

Describe the end behavior of the function: y = x² - 3x

Rises to right and left

200

Describe the end behavior of the function: y = -x³

Falls to the right and rises to the left

300

If a polynomial has 4 turning points, what is the least possible degree?

5

400

Describe the behavior of a zero if it has an odd multiplicity. 

It crosses the x-axis

500

Describe the end behavior of the function and find the y-intercept: y = 7x - 5x² + 8x

Falls to the right and left; (0,0)

Polynomials and Factors

100

Factor the polynomial: y = x³ + 2x² - 9x - 18

y= (x + 3)(x - 3)(x + 2)

200

Write the linear factorization of the polynomial: x⁴ + 7x³ + 10x²

x(x)(x + 5)(x + 2)

300

Convert the polynomial below to intercept/factored form. 

f(x) = 2(x - 1)² - 8

f(x) = 2(x - 3)(x + 1)

400

Write as a product of linear factors, given that (x - 3) is a factor:

f(x)=2x⁴ - x³ + 35x² - 25x - 375

f(x) = (x - 3)(x + 5i)(x - 5i)(2x + 5)

500

Write a polynomial function in standard form with the given zeros: 1, -1, -2i

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

y = x⁴ + 3x² - 4

Solving Polynomial Equations

100

Find all real and imaginary solutions of the polynomial equation: x² + 16 = 0

x = 4i and -4i

200

Find all real and imaginary solutions of the polynomial equation: 3x² + 4x = 7

x = 1 and -7/3

300

Which zero of the polynomial equation would have a multiplicity of two?

 x⁴ - 3x³ - 3x² + 11x - 6 = 0

x = 1

400

Ms. Hanley solved a 7th degree polynomial and found that it had 5 real zeros. Could this be true for this polynomial? Why or why not?

Yes! This would mean you have 2 imaginary zeros. These zeros would be a conjugate pair.

500

Find all real solutions of the polynomial equation: 

x³ - 4x² - 6x = 0

x = 0, 2 + √10, 2 - √10

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

Divide: (2x⁴ + 3x³ - 5x² + 4x + 7) ÷ (x² + 2x - 1)

2x² - x - 1 + (5x + 6)/(x² + 2x - 1)

500

Divide: (3x⁵ - 2x³ + 4x - 7) ÷ (x² - 3)

3x³ + 7x + (25x - 7)/(x² - 3)