Algebra 2 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

Multiplying Polynomials

100

Multiply the Polynomials:

3x² (2x⁴)

 

6x⁶

200

Multiply the Polynomials:

2x(x + 5)

2x² + 10x

300

Multiply the Polynomials:

(2x + 3)(x + 1)

2x² + 5x + 3

400

Multiply the Polynomials:

(y + 5)(y² + 2y - 6)

y³ + 7y² + 4y - 30

500

Multiply the Polynomials:

(4x - 1)(2x² + 6x - 3)

8x³ + 22x² - 18x + 3

600

(x-1)(x+4)(x+5)

x^3+8x^2+11x-20

End Behavior

100

What is the end behavior of the polynomial listed below? (NO DESMOS)

f(x)=x^2

up and up

200

What is the end behavior of the polynomial listed below? (NO DESMOS)

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

up and down

300

What is the end behavior of the polynomial listed below? (NO DESMOS)

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

down and down

400

Where is the function increasing and decreasing? (You can use Desmos.)

x^{3}-10x^{2}+x+52

I: x<0.05 & x>6.6

D: 0.05<x<6.6

500

Where is this function positive and negative?

f(x)=x^{3}-10x^{2}+x+52

+: -2.03<x<2.7 & x>9.3

-: x<-2.03 & 2.7<x<9.3

600

What is the end behavior of the polynomial listed below? (NO DESMOS)

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

down and up

Zeros of Polynomials

100

List the zeros of the function

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

1,-2

200

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

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

x=1/2, -3

300

How many imaginary roots are there? (You can use Desmos)

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

4

400

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

2, 3, -1

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

500

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

-1, 3

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

600

How many real zeros does this polynomial have? (You can use Desmos)

x^3+10x^2+37x+52

1

Naming Polynomials

100

3x+5

Linear Binomial

200

3x³+12x+1

Cubic Trinomial

300

4x^2

Quadratic Monomial

400

8x⁵+x⁴+4x³-2x+1

Fifth Degree Polynomial

500

2x^4 +3x-4

Quartic Trinomial

600

-4x^2-3x+5x^5-7

Quintic Polynomial