Polynomial Function Concepts

what is a factor?

A term that will divide the equation evenly

Factor example:

(x-2)

ways to factor:

-synthetic division

-long division

-GCF

-sum of cubes

-factor by hand

-complete the square

-quadratic formula

*quadratics only

What is a root?

Values of x that make y 0. Also the x-intercepts.

Root example:

x=2

How do you get a root from a factor?

Set the factor equal to 0 and solve for x

How do you get a factor from a root?

Subtract the root from x and put in ()

How to find possible rational roots?

factors of p/ factors of q

what are the factors of p?

the factors of the constant

what are the factors of q?

The factors of the leading coefficient

How to divide with long division?

Divide the polynomial by a factor, if the remainder =0, then it is a factor.

How to divide with synthetic division?

Divide the polynomial by the root, if the remainder=0, then it is a factor.

Overall degree standard form

The highest degree

Overall degree factored form

Add all degrees together

Sum of cubes:

𝑎3+𝑏3=(𝑎+𝑏)(𝑎2−𝑎𝑏+𝑏2)

Difference of squares

There should never be a ____ in a factor

fraction

When a is +…

The right side end behavior is up

When a is -…

The right side end behavior is down

When overall degree is even…

Both sides end behavior is the same

When overall degree is odd…

The sides of end behavior are different

i=

√-1

How do you factor out gcf?

Factor out the GCF, dividing it from the two coefficients and subtracting the exponents of each variable. When both terms are negative, also factor out the negative