tailieunhanh - The sat skill exam 7

Tham khảo tài liệu 'the sat skill exam 7', ngoại ngữ, anh ngữ phổ thông phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | THE SAT MATH SECTION Example 3x 1 7x 10 3x and 7x are the first pair of terms 3x and 10 are the outermost pair of terms 1 and 7x are the innermost pair of terms and 1 and 10 are the last pair of terms. Therefore 3x 7x 3x 10 1 7x 1 10 21x2 30x 7x 10. After we combine like terms we are left with the answer 21x2 37x 10. Factoring Factoring is the reverse of multiplication 2 x y 2x 2y Multiplication 2x 2y 2 x y Factoring Three Basic Types of Factoring Factoring out a common monomial 10x2- 5x 5x 2x- 1 and xy- zy y x- z Factoring a quadratic trinomial using the reverse of FOIL y2- y - 12 y - 4 y - 3 and z2 - 2z 1 z - 1 z - 1 z - 1 2 Factoring the difference between two squares using the rule a2- b2 a b a - b and x2 - 25 x 5 x - 5 Removing a Common Factor If a polynomial contains terms that have common factors the polynomial can be factored by using the reverse of the distributive law. Example In the binomial 49x3 21x 7x is the greatest common factor of both terms. Therefore you can divide 49x3 21x by 7x to get the other factor. 49x3 21x 49x3 I 21x 7 2 _ _ 3 7x 7x 7x Isolating Variables Using Fractions It may be necessary to use factoring in order to isolate a variable in an equation. Example If ax - c bx d what is x in terms of a b c and d 1. The first step is to get the x terms on the same side of the equation. ax - bx c d 2. Now you can factor out the common x term on the left side. x a - b c d 3. To finish divide both sides by a - b to isolate the variable of x. x a - b c d a - b a - b 4. The a - b binomial cancels out on the left resulting in the answer c d x T-t Quadratic Trinomials A quadratic trinomial contains an x2 term as well as an x term. x2 - 5x 6 is an example of a quadratic trinomial. It can be factored by reversing the FOIL method. Start by looking at the last term in the trinomial the number 6. Ask yourself What two integers when multiplied together have a product of positive 6 Make a mental list of these integers 1 X 6 -1 X -6 2 X 3 -2 X -3 Next look at

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