Table of Contents
Methods
Factor Theorems
Remainder Theorem
if dividing by (ax - b), then P(b/a) = 0, it is a factor, if not a factor, than P(b) = remainder
if we want to check if (x+1) is a factor of x^4 - 2x^2 + 3
just, sub in when x = 1, which is -1 in the dividend
(-1)^4 - 2(-1)^2 + 3 = 2
since, this is not equal to 0, it is not a perfect factor, the remainder would be 2.
Factor Theorem
Remainder theorem in practice for finding factors. if f(x) = 0, its a factor
Division Statements
Normal Form
P(x) = divisor * quotient + remainder P(x) = (x-b) * Q(x) + R
Quotient Form
Same as division statement, but we divide everything by our divisor.
MAKE SURE TO STATE THE RESTRICTIONS
Practical Use of Division Statements
Techniques For Finding Factors
Zero Product Rule applies for all of these
Specialized
- Integral Zero Theorem ← Dog Ass
- Rational Root Theorem ← Godsend
- Factor by Grouping Terms
- Newton’s Method ← Last Resort