Algebraic Fractions/Factoring
Simplifying complex fractions
rewrite as (numerator)÷(denominator) preform the operations inside the parenthesis multiply by the reciprocal (factor&cancel)
Factoring Completely
x³+2x²-8x x(x²+2x-8) x(x+4)(x-2)
Degree 4 polynomial
x⁴-20x²+64 Let n=x² n²-20n+64 (n-16)(n-4)
Degree 5 polynomial
x⁵-12x³+32x x(X⁴-12X²+32) Let n=x² **Follow degree 4 procedure**
Un-FOIL
2x²+2x-4 (2x+4)(x-1)
Greatest Binomial Factor
2x²+7x+3 2x²+____+____+3 2x²+x+6x+3 x(2x+1)+3(2x+1) (2x+1)(x+3)
Greatest Common Factor
2x³+6x 2(x²+3)
Difference of 2 squares
9x²-16 (3x+6)(3x-6)
Dividing
Copy the first fraction change from division to multiplication flip the second fraction follow multiplication rule
Simplifying Algebraic Fractions
Factor and cancel factors (x-5) and (5-x) differ by -1
Adding/Subtracting
Rewrite with a common denominator Add/Subtract (subtract entire numerator) Simplify!
