By Alvin K Bettinger; John A Englund

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**Extra resources for Algebra and trigonometry**

**Sample text**

K The Grouping Method The second method for factoring trinomials of the type ax 2 + bx + c, a Z 1, is known as the grouping method, or the ac-method. To factor ax 2 + bx + c, a Z 1, using the grouping method: 1. Factor out the largest common factor. 2. Multiply the leading coefficient a and the constant c. 3. Try to factor the product ac so that the sum of the factors is b. That is, find integers p and q such that pq = ac and p + q = b. 4. Split the middle term. That is, write it as a sum using the factors found in step (3).

Next, try factoring as a sum or a difference of cubes. There is no rule for factoring a sum of squares. Three terms: Try factoring as the square of a binomial. Next, try using the FOIL method or the grouping method for factoring a trinomial. Four or more terms: Try factoring by grouping and factoring out a common binomial factor. k C. Always factor completely. If a factor with more than one term can itself be factored further, do so. 4 Exercise Set 13. 24x 3 - 36x 2 + 72x - 108 Factor out the largest common factor.

The distance from Earth to the sun is defined as 1 astronomical unit, or AU. It is about 93 million mi. 1 AUs (Source: Astronomy Department, Cornell University). How many miles is it from Earth to Neptune? Express your answer in scientific notation. 01 * 10. 993>10. 7993 * 109 mi. 7993E9 Now Try Exercise 79. 3 Order of Operations Recall that to simplify the expression 3 + 4 # 5, we first multiply 4 and 5 to get 20 and then add 3 to get 23. Mathematicians have agreed on the following procedure, or rules for order of operations.

### Algebra and trigonometry by Alvin K Bettinger; John A Englund

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