1: Prerequisites
In this chapter, we will review sets of numbers and properties of operations used to manipulate numbers. This understanding will serve as prerequisite knowledge throughout our study of algebra and trigonometry.
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- 1.0: Prelude to Prerequisites
- Measuring and recording the characteristics of weather conditions requires a use of different kinds of numbers. Calculating with them and using them to make predictions requires an understanding of relationships among numbers. In this chapter, we will review sets of numbers and properties of operations used to manipulate numbers. This understanding will serve as prerequisite knowledge throughout our study of algebra and trigonometry.
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- 1.5: Factoring Polynomials
- The greatest common factor, or GCF, can be factored out of a polynomial. Checking for a GCF should be the first step in any factoring problem. Trinomials with leading coefficient 1 can be factored by finding numbers that have a product of the third term and a sum of the second term. Trinomials can be factored using a process called factoring by grouping. Perfect square trinomials and the difference of squares are special products and can be factored using equations.
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- 1.6: Rational Expressions
- The quotient of two polynomial expressions is called a rational expression. We can apply the properties of fractions to rational expressions, such as simplifying the expressions by canceling common factors from the numerator and the denominator. To do this, we first need to factor both the numerator and denominator.
Thumbnail: A shortcut called FOIL is sometimes used to find the product of two binomials. It is called FOIL because we multiply the first terms, the outer terms, the inner terms, and then the last terms of each binomial.