Polynomials - Copy

Standard Form

100

What are the 2 rules for Standard Form?

Terms must be in Alphabetical Order, and Exponents in Descending Order

200

What always comes last in Standard Form?

Constants

300

Is this in Standard Form? If not, what needs to be fixed?

4a^3+2b^2-3a+7

-3a needs to come before 2b^2

400

Put this expression in Standard Form.

2a^2+7b^3-7-3a^3+4b^2

-3a^3+2a^2+7b^3+4b^2-7

500

Put this expression in Standard Form

-3m^2n^2+8mn^3+m^3n

m^3n-3m^2n^2+8mn^3

1000

Write this expression in Standard Form.

14a^2+5a^3b^2-9a^3+12a^2b^3-3ab^2+8a^3

-a^3+14a^2+5a^3b^2+12a^2b^3-3ab^2

Classifying Polynomials

100

What are the 2 things that we use to determine the classification of a polynomial?

Degree and the number of terms

200

What determines the Degree of a polynomial?

The highest exponent in the expression

300

Classify this polynomial

3x+12

Linear Binomial

400

Classify this polynomial

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

Cubic Polynomial

500

Classify this polynomial

x^4-24

Quartic Binomial

1000

Give an example of a quadratic binomial.

Answers may vary.

Adding Polynomials

100

When we add polynomials, what is the rule that we follow, that says we must make sure the terms we add have the same variable and the same exponent?

Combine Like Terms.

200

Add these polynomials

(-4x+3)+(-3x-5)

-7x-2

300

Find the sum of these polynomials

(3a^2-a+3)+(4a^2-5)

7a^2-a-2

400

Find the sum

(5w^3-w+2w^2+4)+(3w^2+1-4w)

5w^3+5w^2-5w+5

500

Find the Sum of 

(2x^2-6x-2) and (x^2+4x)

3x^2-2x-2

1000

Find the sum of

(3y^2 – 4y + 1) + (-y^2 + y – 2)

2y^2-3y-1

Subtracting Polynomials

100

If we subtract Polynomials, what does the minus sign do to the second set of parentheses?

It distributes a negative to all terms in the parentheses.

200

Find the Difference

(7p^2+3p)-(5p^2+4)

2p^2+3p-4

300

Find the Difference

(8r^2-12r+4)-(3r^2+5r-1)

5r^2-17r+5

400

Subtract 

(-a^2-5ab+3b^2) f rom (3a^2-2ab+3b^2)

4a^2+3ab

500

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

5x^2+y^2

1000

Find the difference

(6x^2 – 5x) – (4x^2 – 3x + 4)

2x^2-8x-4

Multiplying Polynomials

100

When multiplying Polynomials, what exponent rule are we using?

Product Rule

200

When we multiply a monomial to a polynomial, what math property do we utilize to multiply multiple items?

Distributive property

300

Multiply

a(4a+3)

4a^2+3a

400

Multiply

-c(11c + 4)

-11c^2-4c

500

Multiply

7c(c^3 – 2c^2 + 5)

7c^4-14c^3+35c

1000

Multiply and Simplify

4n(3n^2 + n – 4) – n(3 – n)

12n^3+5n^2-19n