Review for Solving Polynomials Quiz - Alg. II H

Finding Roots

100

2X³+13x²+17x-5 = 0 

x = 1/2, -3, -4

200

4X³ - 12x² - x + 3

x = 3, + 1/2 and -1/2

300

x⁶ - 7x⁵ - 13x⁴ + 39x³ + 16x² - 68x + 32

x = 8 

x= 1 (3) 

x = -2 (2) 

400

x⁶ + 8x⁵ + 13x⁴ = 40x³ + 117x² - 135

x = 1 

x = -3  (3)

x = + or - sqrt(5) 

500

x⁶ - 4x⁴ - 81x² + 324

x = 2

x = 3 

x = -2 

x = -3 

x = + or - 2i 

Rational Roots

100

Name 2 additional roots if 4i and 2+i are both roots

-4i and 2-i

200

Find a standard form equation of a polynomial that has a root of 2i and a degree of 2. 

(x²+4)

300

write a standard form polynomial of degree 3 that has roots of 3i and 2 

(x²+9) (x-2)

x³ - 2x² + 9x -18 

400

Find a 4th degree polynomial with roots of 2i and 

sqrt (3)

(x²-3) (x²+4) 

x⁴ + x² - 12

500

Find a 4th degree polynomial with roots of 

2i and 3+i

x⁴ - 6x³ + 14x² -24x + 40

Factoring

100

x³-27

(x-3) (x² + 3x + 9)

200

4x² - 169

(2x + 13) (2x - 13) 

300

8x³ + 125

(2x + 5) (4x² - 10x +25) 

400

900x² - 1,000,000

(30x - 1000) (30x + 1000)

500

216x³ - 27a¹⁵b⁹c⁶

(6x - 3a⁵b³c²) (36x² + 18xa⁵b³c² + 9a¹⁰b⁶c⁴) 

Misc Math Questions

100

Identify the possible roots of x⁵ + 4x⁴ - 5

+/- (5, 1)

200

Identify the possible roots of 3x³ - 4x⁵ + 3 + 6x

+/- (3, 3/4, 1, 1/4, 3/2, 1/2) 

300

How solutions will the following polynomial have? What is the name of the theorem that proves that? 

x⁷ - 5x = 0 

7 - fundamental theorem of algebra 

400

Simplify the following

(5+i) / (4+i)

(21-i) / 17

500

Find 3 consecutive even integers whose product is -48

-2, -4, -6 

Miscellaneous College Trvia

100

Name 5 colleges / universities located in BOSTON

BC, BU, NEU, Berklee, Suffolk, MCPHS, UMB, Emerson, Wentworth Etc.

200

Can you name 3 NESCAC colleges? (New England Small College Athletic Association). 

Bates, Bowdoin, Colby, Middlebury, Williams, Hamilton (NY), Conn College, Amherst College, Trinity, Tufts, Weslayan

300

Which college major on average has the highest LSAT score? (Law school entrance exam) 

Statistics / Mathematics (168) 91st percentile 

400

How many Ivy league schools are there? Name them all. 

Cornell, Darmouth, Harvard, Penn, Princeton, Brown, Yale

8! 

500

Name a city in the U.S. With a population between 1.5 and 2 million people. And name 1 college located in the metropolitan area of that city! 

Phoenix, Philly, San Antonio

Nova, Temple, St. Joes, AZ State, UTSA