Algebra 2 Honors Polynomials

Adding Polynomials

100

Add the Polynomials

(4x + 9) +(x - 4)

5x + 5

200

Add the polynomials:

(-3a - 2) + (7a + 5)

4a + 3

300

Add the polynomials:

(x² +3x + 5) + ( -x² +6x)

9x + 5

400

Add the polynomials:

(t² + 3t³ -3) + (2t² +7t -2t³) 

t³ +3t² +7t -3

500

Add the polynomials: 

(-1 + x² + 2x) + (1 -2x + 2x²)

3x²

600

Add the polynomials:

 (2x² + 6y + 3xy) + (3x² - 5xy - x) 

5x² - x + 6y - 2xy 

Subtracting Polynomials

100

Subtract the polynomials:

(g - 4) - (3g - 6)

-2g + 2

200

Subtract the polynomials:

(-5h - 2) - (7h +6)

-12h - 8

300

Subtract the polynomials:

(-x² - 5) - (-3x² -x -8)

2x² + x +3

400

Subtract the Polynomials:

(k² + 6k³ -4) - (5k³ + 7k -3k²)

k³ + 4k² -7k -4

500

Subtract the Polynomials:

(2x - 3x) - (x² -2x + 4)

-x² + x - 4

600

Subtract the following polynomials

(3 - 6x⁵ - 8x⁴) - (-6x⁴ - 3x - 8x⁵)

2x⁵ - 2x⁴ + 3x + 3

Dividing Polynomials

100

Divide the polynomial:

(m^2 − 7m − 11) ÷ (m − 8)

 

m + 1 − 3/(m − 8

200

Divide the Polynomial:

(n^2 − n − 29) ÷ (n − 6)

n + 5 + 1/( n − 6

300

Divide the polynomial:

(x^ 2 − 74) ÷ (x − 8)

x + 8 − 10/( x − 8

400

Divide the polynomial:

(x ^3 − 13x^ 2 + 40x + 18) ÷ (x − 7)

x^ 2 − 6x − 2 + 4/( x − 7

500

Divide the polynomial:

(v ^3 − 2v^ 2 − 14v − 5) ÷ (v + 3)

v^ 2 − 5v + 1 − 8/( v + 3

600

Divide the Polynomials:

(50k^ 3 + 10k^ 2 − 35k − 7) ÷ (5k − 4)

10k^ 2 + 10k + 1 − 3/( 5k − 4

End Behavior

100

What is the end behavior of the polynomial listed below?

f(x)=x^2

up and up

200

What is the end behavior of the polynomial listed below?

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

up and down

300

What is the end behavior of the polynomial listed below?

f(x)=-67x^1002-67x^67+67x^76+67

down and down

400

What does an even multiplicity do on a graph?

bounce

500

What is the end behavior of the polynomial listed below?

f(x)=7x^9+12x^8+11x^7-x^6+3x^5-11x^11+12x^4-9x^3+92x^2+x-19

up and down

600

What is the end behavior of the following function?

y=3x-2

down and up

Zeros of Polynomials

100

List the possible zeros of the function

f(x)=5x^4+11x^2+2

+-1,+-2,+-1/5,+-2/5

200

If 1 is a zero of the polynomial listed below, what are the other two zeros?

f(x)=5x^3-x^2-5x+1

x=-1,1/5

300

If you were given the function below, how many zeros would you need at a minimum to find using the synthetic division method?

f(x)=8x^6+65x^3+8

Four, because after that it is a quadratic.

400

Write a polynomial function of the least degree with integral coefficients with the given zeros.

2, 3, -1

y=x^3-4x^2+x+6

500

Write a polynomial function of the least degree with integral coefficients with the given zeros.

-1, i

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

600

Write a polynomial function of the least degree with integral coefficients with the given zeros.

-4, -3+2i

f(x)=x^3+10x^2+37x+52