tailieunhanh - The gre anlytycal writting section 7

Tham khảo tài liệu 'the gre anlytycal writting section 7', ngoại ngữ, anh ngữ phổ thông phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | THE GRE QUANTITATIVE SECTION Removing a Common Factor If a polynomial contains terms that have common factors you can factor the polynomial by using the reverse of the distributive law. Example In the binomial 49x3 21 x 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 21x 2 7x 7x 7x x Thus factoring 49x3 21x results in 7x 7x2 3 . Isolating Variables Using Fractions It may be necessary to use factoring to isolate a variable in an equation. Example If ax - c bx d what is x in terms of a b c and d The first step is to get the x terms on the same side of the equation ax - bx c d Now you can factor out the common x term on the left side x a - b c d To finish divide both sides by a - b to isolate x x a-b c d a b a b The a - b binomial cancels out on the left resulting in the answer c d x 7-r 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. Reverse the FOIL method to factor. 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 and -2 X -3 Next look at the middle term of the trinomial in this case the negative 5x. Choose the two factors from the above list that also add up to negative 5. Those two factors are -2 and -3. Thus the trinomial x2 - 5x 6 can be factored as x - 3 x - 2 . Be sure to use FOIL to double check your answer. The correct answer is x - 3 x - 2 x2 - 2x - 3x 6 x2 - 5x 6 170 ------------------------- THE GRE QUANTITATIVE SECTION --------------------------------- Algebraic Fractions Algebraic fractions are very similar to fractions in arithmetic. Example Write x - as a single fraction. Solution Just like arithmetic you need to find the LCD of 5 and 10 which is 10. Then change each fraction into an equivalent fraction that has 10 as a denominator 5