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Properties of Exponents
*Any variable or number to the zero power = 1, always. exponent - The exponent of a number shows you how many times the number is to be used in a multiplication. It is written as a small number to the right and above the base number Properties:
Addition: cx a + dx a = (c + d )x a
Subtraction: cx a - dx a = (c - d )x a
Multiplication: cx a×dx b = (cd )x a+b
Division: = ()x a-b
Distribution: (cd )a = c a d a
Power of a Power: c(x a)b = cx ab -
Period: to
Unit 5
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Monomials
Monomial - a constant, a variable, or the product of a constant and a variable. Example: 3x^2 *Like terms, or similar terms, are terms which differ only in numerical coefficients Addition of monomials
ax^by^d + cx^by^d = (a+c)x^by^d Subtraction of monomials
ax^by^d - cx^by^d = (a-c)x^by^d Multiplication of monomials
(3a^3b^2c^1)(2a^1b^2c^3) = 6a^3b^5c^4 Division of monomials
(6a^2b^3c^4) / (2a^1b^2c^2) = 3a^1b^1c^2 -
Polynomials
Polynomial - a finite sum of terms where the exponents on the variables are non-negative integers binomial - a polynomial with 2 terms
trinomial - a polynomial with 3 terms *terms are separated by +'s and -'s. *always put polynomial in descending order by degree, and combine like terms Adding and subtracting polynomials
(10x^2 - 3x +7) + (3x^2 - 4x +8) = 13x^2 -7x +15
(10x^2 - 3x +7) - (3x^2 - 4x +8) = 7x^2 +x - 1
*distribute the negative to each term inside the second polynomial -
Factoring Polynomials (4+ Terms)
GCF - greatest common factor *write a polynomial in factored form using the distributive property Factoring by Grouping (use for polynomials with 4+ terms)
2b^3 + 3a^3 + 3ab^2 + 2a^2b = (2b^3 + 2ab^2) + (3a^3 +3ab^2) = 2b(a^2 + b^2) + 3a(a^2 + b^2) = (2b + 3a)(a^2 + b^2) * -
Factoring Polynomials
*always factor our GCF first Factoring Trinomials in form x^2 + bx + c
(x + _ )(x + _ ) or (x - _ )(x - _ ) ; for any positive c, and
(x + _ )(x - _ ) or (x - _ )(x + _ ); for any negative c Factoring Trinomials in form ax^2 +bx +c, where a > 1
use reverse foil and trial and error
( )( ) Factoring a Perfect Square Trinomial
a^2 + 2ab + b^2 = (a+b)^2
a^2 - 2ab + b^2 = (a-b)^2
