Standard Form
What are the 2 rules for Standard Form?
Terms must be in Alphabetical Order, and Exponents in Descending Order
What are the 2 things that we use to determine the classification of a polynomial?
Degree and the number of terms
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.
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.
When multiplying Polynomials, what exponent rule are we using?
Product Rule
What always comes last in Standard Form?
Constants
What determines the Degree of a polynomial?
The highest exponent in the expression
Add these polynomials
(-4x+3)+(-3x-5)
-7x-2
Find the Difference
(7p^2+3p)-(5p^2+4)
2p^2+3p-4
When we multiply a monomial to a polynomial, what math property do we utilize to multiply multiple items?
Distributive property
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
Classify this polynomial
3x+12
Linear Binomial
Find the sum of these polynomials
(3a^2-a+3)+(4a^2-5)
7a^2-a-2
Find the Difference
(8r^2-12r+4)-(3r^2+5r-1)
5r^2-17r+5
Multiply
a(4a+3)
4a^2+3a
Put this expression in Standard Form.
2a^2+7b^3-7-3a^3+4b^2
-3a^3+2a^2+7b^3+4b^2-7
Classify this polynomial
-x^3+5x^2+x-7
Cubic Polynomial
Find the sum
(5w^3-w+2w^2+4)+(3w^2+1-4w)
5w^3+5w^2-5w+5
Subtract
(-a^2-5ab+3b^2) f rom (3a^2-2ab+3b^2)
4a^2+3ab
Multiply
-c(11c + 4)
-11c^2-4c
Put this expression in Standard Form
-3m^2n^2+8mn^3+m^3n
m^3n-3m^2n^2+8mn^3
Classify this polynomial
x^4-24
Quartic Binomial
Find the Sum of
(2x^2-6x-2) and (x^2+4x)
3x^2-2x-2
(2x^2+3y^2-z^2)-(x^2-y^2-z^2)+(4x^2-3y^2)
5x^2+y^2
Multiply
7c(c^3 – 2c^2 + 5)
7c^4-14c^3+35c
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
Answers may vary.
Find the sum of
(3y^2 – 4y + 1) + (-y^2 + y – 2)
2y^2-3y-1
Find the difference
(6x^2 – 5x) – (4x^2 – 3x + 4)
2x^2-8x-4
Multiply and Simplify
4n(3n^2 + n – 4) – n(3 – n)
12n^3+5n^2-19n