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Chapter 2: Polynomial Functions (Factoring polynomials (grouping: use a…
Chapter 2: Polynomial Functions
Synthetic and Long Division
Synthetic: short cut method to long division
use a root to multiply the coefficients and then add down each column.
ex:
Long
used to determine if something is a factor or not, also can find remainder.
ex:
graphing polynomials
single root: goes through x axis once. Raised to the 1st power
ex: y=(x+2)(x-2)(x-4)
double root: bounces on axis and goes back. Raised to 2nd power
ex: y=(x+5)^2(x-1)
triple root: goes through the x-axis in the shape of a cubic function. Raised to the 3rd power
ex: y=-(x+1)^3(x-3)
Factoring polynomials
grouping: use a common coefficient ration and an even number of terms in order to factor out the roots.
greatest common factor: factor out the gcf of a polynomial.
quadratics in disguise: use a dummy variable, such as w, to x. make sure you square root it after
rational root theorem: find all the multiples of the last coefficient and divide them by all the multiples of the first coefficient in order to find all of the possible rational roots.
