Algebra 1 Polynomial Review

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

(3x+2)+(4x-2)+(x^2-x)

(x^2+6x)

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

Exponent Rules

100

When multiplying the same base, we __________ the exponents

Add

200

Simplify:

x^4* x^7

x¹¹

300

When dividing the same bases, we ___________ the exponents.

Subtract

400

Simplify:

y^10/y^4

y⁶

500

When a term is raised to another power, we _________ the exponents

Multiply

600

Anything to the power of zero is....

1

Multiplying Polynomials

100

Multiply the Polynomials:

3x² (2x⁴)

6x⁶

200

Multiply the Polynomials:

3(2x + 4x² - 5)

12x² + 6x - 15

300

Multiply the Polynomials:

−y² (−8x² − 6xy − y² )

8y²x² + 6y³x + y⁴ 

400

Multiply the Polynomials:

(x-2)(x+6)

x²+4x-12

500

Multiply the Polynomials:

(3x-6)(5x+3)

15x²-21x-18

600

Multiply the following polynomials

(3r+ 5)²

9r² + 30r + 25

Vocab

100

The largest exponent of a polynomial is called the ...

Degree

200

The coefficient of the term with the largest exponent is called the...

Leading coefficient

300

When a polynomial is written with exponents in descending order...

Standard Form

400

Write the following in standard form:

3x + 4x^4 -10x^2 -5

4x^4 - 10x^2 + 3x -5

500

Identify the degree of the following polynomial

3x^2 - 10x^5 + 7x -8

5

600

Identify the leading coefficient and constant term:

3x^2 - 10x^5 + 7x -8

leading coefficient: -10

constant term: -8