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!