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Exponent Rules
Find Degree/Classify
Combining Like Terms
Polynom. Multiplic.
BOX Method
100
2^-3
1/8
100
How do you find the degree of a monomial? How do you find the degree of a polynomial?
Monomial: Add the exponents Polynomial: Take the greatest exponent
100
Add the like terms: (3x^2 - 2x +8) - (x^2 - 4)
2x^2 - 2x +12
100
Multiply the monomials: (5x^2)(4x^3)
20x^5
100
Multiply: (x-5)(x-5)
x^2 - 10x + 25
200
a^0b^-3
1/b^3
200
What is the degree of this polynomial? 7x^2 - 4x +5y How many terms does it have?
Degree: 2 Terms: 3
200
Add the like terms: 15m^3 + 6m^2 +2m^3
17m^3 + 6m^2
200
Multiply the monomials: (-3x^3y^2)(4xy^5)
-12x^4y^7
200
Multiply: (m + 1)(m + 1)
m^2 + 2x +1
300
3y^-2
3/y^2
300
What is the degree of this monomial? 5x^3y How many terms does it have?
Degrees: 4 Terms: 1
300
Add the like terms: (-2ab + b) + (2ab +a)
b + a
300
Multiply the monomial by the polynomial: 2x^2y(3x-y) Hint: use distribution
6x^3y - 2x^2y^2
300
Multiply: (5x - 2)(x +3)
5x^2 + 13x - 6
400
(7^4)^3
7^12 = 823,543
400
This degree of this polynomial is 3, and it has 3 terms. What words do you use to classify it? 3x^3 + 6x^2 - 5
Cubic Trinomial Cubic: (3 degrees) Trinomial: (3 terms)
400
Subtract the like terms: (a^4 -2a) - (3a^4 - 3a +1)
-2a^4 + a -1
400
Multiply: 4a(a^2b + 2b^2) Hint: Use distribution
4a^3b + 8ab^2
400
Multiply: (2a +7b)(2a +7b)
7a^2 +28ab + 49b^2
500
(x^-2y^0)^-3
What is 1/x^6
500
Put this cubic binomial in standard form. (x - 2y^4) What is the leading coefficient?
(-2y^4 +x) Leading coefficient: -2
500
Subtract the like terms: (11z^3 - 2z) - (z^3 - 5)
10z^3 - 2z +5
500
Multiply: 3ab(5a^2 +b)
15a^3b + 3ab^2
500
Multiply: (s^2 - 7)(s^2 - 7)
s^4 - 14s^2 + 49