Polynomial Review -Lessons 7.1-7.4 & 7.7

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

Name it!

100

Name this polynomial:  3x² + 5

Quadratic Binomial

200

How many terms are in a Cubic trinomial?

3

300

What is the degree of this monomial:   5x⁴y⁵z

10

400

Find the degree of the polynomial: 7x²y³ + 5xz² - 3y²

5

500

Is 2 a monomial or a constant?

BOTH!

600

Put this in standard form and name it:

4x³ - 1 - 2x + 3x² - 7 + x + 7x² - 9x³ + 8 + x

-5x³ + 10x² 

Cubic Binomial

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)²

9x² -36x + 36

600

Multiply the following polynomials

(3r + 5)(4r² + 3r + 3)

12r³+29r²+24r +15

Mult. Special Cases

100

Multiply (x+5)(x-5)

x² - 25

200

Simplify

(3x + 7)²

9x² + 42x + 49

300

(4x - 3y)(4x + 3y)

16x² - 9y²

400

(11xy - 5z)²

121x²y² - 110xyz + 25z²

500

(9z³ - 7y⁴)(9z³ + 7y⁴)

81z⁶ - 49y⁸

600

Mental math:  (SHOW THE SPECIAL PRODUCTS)

42²

AND

57 * 63

(40 + 2)² = 1600 +160 + 4 = 1764

AND

(60-3)(60 +3) = 3600 - 9 = 3591

Special Cases

100

Factor: x² + 10x + 25

(x + 5)²

200

Factor:  9x² - 42x + 49

(3x - 7)²

300

Factor: 4x² - 49

(2x - 7)(2x + 7)

400

Factor:    25x² + 90xy + 81y²

(5x + 9y)²

500

Factor completely:  81x⁸ - 16y⁴

(9x⁴ + 4y²)(3x² + 2y)(3x² - 2y)

600

Factor Completely:   98x²y⁴ - 18z⁸

2(7xy² - 3z⁴)(7xy² + 3z⁴)