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Advanced Functions Unit 1

Polynomial Functions

Quintic

f(x) = ax^5

Quartic

f(x) = ax^4

Cubic

f(x) = ax^3

Quadratic

f(x) = ax^2

Linear

f(x) = ax

Polynomial Functions in general form:

f(x) = a(nx)^n + a(n-1)x^(n-1) + a(n-2)x^(n-2) + ... a(3)x^3 + a(2)x^2 + a(1)x + a

Notes: -

Factoring

Sum of Cubes

f(x) = a^3 + b^3 = (a + b)(a^2 - ab + b^2)

Difference of Cubes

f(x) = a^3 - b^3 = (a-b)(a^2 + ab + b^2)

Difference of Squares

f(x) = a^2 - b^2 = (a+b)(a-b)

Factoring less simple trinomials

f(x) = ax^2 + bx +c (where a =/ 1) (DON'T FORGET TO GROUP FACTOR)

Factoring Simple Trinomials

f(x) = x^2 + bx + c (where a = 1)

Common Factoring

f(x) = ax^2 + bx (factor out commonality in each term)