The Algebra II Dictionary Noah Trevino, Sara Turpin, Jasmine Salinas, and Quentin Bonner

One & Zero as Exponents Rules If one is the exponent keep the base. If zero is the exponent the whole power becomes one. Examples B 1 = B B 0 =1

Negative Exponents Rules If the exponent is negative, take the reciprocal of the power. Example b -n = 1/b n OR 1/b -n = b n

Product Of A Power Rules To Multiply Powers With The Same Base Keep The Base, Add Exponents. Example b n * b m = 6 n+m

Power To a Power Rules Keep the base and multiply the exponents Examples (b n ) m =b n*m

Quotient of Powers Rules To find the quotient of an exponent keep the base and subtract the exponents. Examples b n /b m =b n-m

Roots as Powers Rules Write the inverse of an exponent as the multiplicitive inverse of the power Examples 3 √27=3

Distribution Follow these steps: o 6(x 2 +3) o 6x What we did: o Start with original problem o Multiply the outside number with each inside term

Polynomials Rules Polynomial: monomial or the sum of monomials Monomials (Term): constants & variables multiplied together to the same power Like terms: terms with same variables to the same powers Variables: symbol to represent a value that changes Constant: number that doesn't change. coefficient: number multiplied by a variable Examples 4x 2 - 4x + 7 3x 3 + 2x 2 + 7x + 4 2x 2 + x + 4

Degrees of Polynomials Rules Polynomials has 2 Standard forms o Variables are in alphabetical order o Terms are in order of degree The degree of the polynomial is the power of the highest term (monomial) in the expression. The degree of a term is calculated by adding all powers of all variables. Example 2y+3f-z should be 3f+2y- z a 2 +y 4 should be y 4 +a 2 2x 2 +x+4 2 nd degree polynomial -2xy 2 z 3 would be a 6th degree monomial

Classifying Numbers

Identities Rules Additive: Number you can add to a number to make it stay the same (0, Always) Multiplicative: Number you can multiply by any number to make it stay the same (1, Always) Examples 374+0= *1=373485

Inverses Rules Additive: Number you add to a number to take it back to 0, the identity (Opposite) Multiplicative: Number you can multiply to take it back to 1, the identity (Reciprocal) Examples 85-85=0 85 x 1/85=1