Math 105 Week 3 Notes
Math 105 Week 3 Notes MATH 105
Edinboro University of Pennsylvania
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This 2 page Class Notes was uploaded by Cassandra Notetaker on Saturday February 6, 2016. The Class Notes belongs to MATH 105 at Edinboro University of Pennsylvania taught by Dr. Phillip Funtulis in Spring 2016. Since its upload, it has received 26 views. For similar materials see College Algebra in Mathematics (M) at Edinboro University of Pennsylvania.
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Date Created: 02/06/16
MATH 105 Funtulis Multiplying Binomials and Trinomials 2/1/16 Like Terms terms with the same variable combination and the same exponents on variables. Ex. 3xyz and 1xyz are like terms. Factor an individual part of a product; factoring is the reverse of multiplying, meaning the final product is factored to arrive at the factors we started with. The FOIL Method: example (x + 2) (x + 1) First = x times x = x^2 Outer = x times 1 = x Inner = 2 times x = 2x Last = 2 times 1 = 2 Then combine like terms. Result: x^2 + 3x + 2. The Distributive Rule: A term on the outside of the parentheses (or other grouping symbol) that is not separated from the parentheses by addition or subtraction is distributed into the parentheses. Example: (x + 2) (x + 1) can be written as x (x + 1) + 2 (x + 1). The x is multiplied into (x + 1) and the 2 is multiplied into (x + 1). The result is x^2 + x + 2x + 2, or x^2 + 3x + 2. **Multiplying a binomial by a trinomial works in a similar fashion. Ex. (x + 2) (x^2 + 4x + 4) distribute the x from (x + 2) to the x^2 , 4x , and 4 in the trinomial. Then distribute the 2 from the (x + 2) in the same way. Combine like terms to arrive at final answer.** MATH 105 Funtulis Special Cases 2/3/16 Degree the highest power of the variable (simple case); when using multiple variables, the highest sum of the variables. Leading Coefficient coefficient of leading or highest power term. Greatest Common Factor the term you can factor out of each part of the equation. Ex. 8x^2 + 16x +24; GCF is 8. Equation can then be written as 8 (x^2 + 2x + 3). When factoring quadratic expressions (x^2 + bx + c) with a leading coefficient of 1, we look for two numbers that multiply to c and add to b. Difference of Squares: a^2 – b^2 = (a – b) (a + b) **Anything that factors into real numbers crosses the xaxis when graphed.** Special Products: (a + b)^2 = (a + b ) (a + b) or a^2 + 2ab + b^2 (a – b)^2 = ((a – b) (a – b) or a^2 – 2ab + b^2
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