Algebra 2
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Forms of Polynomials
Expression: 2x + 8
Equation: 2x – 3 = 5 This equation is true when x = 4 only. It is true for only one value of the independent variable.
Identity: 3x – 9 = 3(x – 3), true for all values of x. In an identity all coefficients of like terms on each side are equal.
Simplifying Equations
An equation must be simplified before it can be solved. The steps involved depends on the complexity of the equation.
- Remove brackets by multiplying
- Bring every term to one side of the equation
- Combine terms by either addition or subtraction
- Rearrange in order of decreasing exponents
If the equation contains quotients then the following steps must be carried out first.
- Find the LCM of the denominators of the equation
- Multiply each term by the LCM and divide factors in order to simplify
LCM = 12
If the equation contains rational polynomial terms then the following steps must be carried out first.
- Factorise the denominators if possible
- Divide any factors within each term if possible
- Find the LCM of the denominators of the equation
- Multiply each term by the LCM and divide factors in order to simplify
