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Cubic, Square Root and Rational Functions. Factor Cubics. Radical Expressions & Equations. Rational Expressions & Equations. How do we factor cubics?. How do we simplify radical expressions?. How do we add, subtract, multiply, divide and simplify rational expressions?.

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Cubic, Square Root and Rational Functions


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Cubic, Square Root and Rational Functions

Factor Cubics

Radical Expressions & Equations

Rational Expressions & Equations

How do we factor cubics?

How do we simplify radical expressions?

How do we add, subtract, multiply, divide and simplify rational expressions?

Product Property of Radicals:

Quotient Property of Radicals:

Radical Conjugates:

Special Product Patterns:

(x + y)3 = x3 + 3x2y + 3xy2 + y2

(x − y)3 = x3 − 3x2y + 3xy2 − y2

Factor Out a Monomial GCF:

2x3 − 6x2y + 6xy2 − 2y2

= 2(x3 − 3x2y + 3xy2 − y2)

=2(x – y)3

Multiple Variables:

a3b3 + 12a2b2 + 4ab +64

= (ab + 4)3

  • Rational expressions arethe ratio of 2 polynomials.
  • Add, subtract, multiply & divide as for any fractions.
  • Then, factor (if needed) & simplify.
  • Check for excluded values.

How do we solve rational equations?

How do we solve radical equations?

  • Use the Cross ProductsProperty to solve as for aproportion.
  • Multiply by the LCD to eliminate denominators.
  • Isolate radical.
  • Square both sides.
  • Simplify and solve.
  • Check for extraneous solutions.

FACTOR: SIMPLIFY: SOLVE: SIMPLIFY: SOLVE:

8x3 + 12x2y +6xy2 + y3