Part 2 Math Project Unit 2

Parts and Operations of Polynomials

100

Find the product 

(x-5)(x+1)

x²-4x-5

200

Find the difference.

(3- 2x + 2x²) - (4x -5 +3x²)

-x² -6x + 8

300

 Find the sum

(2x² + 5x - 7) + ( 3 - 4x² + 6x)

-2x² + 11x -4

400

Name the Degree, Leading Coefficient, Leading term, and Constant of the following polynomial: 

 3x⁷-5x⁴+8x-10

Degree: 7

Leading Coefficient: 3

Leading Term: 3x⁷

Constant: -10 

500

Add the following polynomials

(2x² + 6x + 5)+(3x² − 2x − 1.)

5x² +4x + 4

Dividing Polynomials

100

Divide the following polynomials 

(x²-3x+2)/(x-2)  

x-1

200

Divide the following polynomials 

 (x³+2x²-2x-1)/(x-1)

x²+3x+1

300

Divide the following polynomials

 (3x²+3x-18)/(x-2)

(3x+9)

400

Divide the following polynomials

 (2x³ + 5x² + 9) ÷ (x + 3)

2x² - x + 3

500

Divide the following Polynomials

(4x² - 24x + 35) ÷ (2x - 5)

2x - 7

The Binomial Theorem and Pascals Triangle

100

Using the Pascal's Triangle, expand the binomial 〖(a + b)〗^6

a6 + 6a5b + 15a4b2 + 20a3b3 + 15a2b4 + 6ab5 + b6

200

What is the sum of the terms in row 6?

 

64

300

What are the terms in row 8 of pascals triangle 

1 8 28 56 70 56 28 8 1

400

How many terms will the binomial expansion of (〖(a - 2√3)〗^11 have?

12

500

What is the 3rd term of the binomial expansion of 〖(a - 2√3)〗^6 ?  

180a4

Combining Functions

100

f(x)=x²+4x
g(x)=2x-3
Find f(x)∙g(x)

2x³+5x²-12x

200

f(x)=x-2
g(x)=x-3
Find f(x)∙g(x)

x²-5x+6

300

f(x)=x-1
g(x)=3x-2
Find g(x)-f(x)

2x-1

400

g(x)=3x+1
h(x)=4x-1
Find g(x)+h(x)

7x

500

f(x)=-x-3
g(x)=x²+x
Find f(g(x))

-x²-x-3

Composing Functions

100

g(x)=-20-3x
h(x)=2-(1/2)^x
Find (g o h)(-2).

-14

200

If f(x) = x2 + 1 and g(x) = x - 4, which value is equivalent to (f o g)(10)?

37

300

If h(x) = x - 7 and g(x) = x2, which expression is equivalent to (g o h)(5) ?

(5 - 7)^2

400

 f(x) = 3x + 2 and g(x) = x2 + 1, which expression is equivalent to (f o g)(x)?  

3(x^2 + 1) + 2

500

h(x)=3(x+3)^2 -11
f(x)=-2x^2 -5x+1
Find h(f(-1)).

136