tailieunhanh - Sat math essentials_4

Tham khảo tài liệu 'sat math essentials_4', ngoại ngữ, anh ngữ phổ thông phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | ALGEBRA REVIEW Monomials A monomial is an expression that is a number a variable or a product of a number and one or more variables. 6 y 5xy2 19a6b4 Polynomials A polynomial is a monomial or the sum or difference of two or more monomials. 7y5 6ab4 8x y3 8x 9y z Operations with Polynomials To add polynomials simply combine like terms. Example 5y3 2y 1 y3 7y 4 First remove the parentheses 5y3 2y 1 y3 7y 4 Then arrange the terms so that like terms are grouped together 5y3 y3 2y 7y 1 4 Now combine like terms Answer 6y3 5y 3 Example 2x 5y 8z 16x 4y 10z First remove the parentheses. Be sure to distribute the subtraction correctly to all terms in the second set of parentheses 2x 5y 8z 16x 4y 10z Then arrange the terms so that like terms are grouped together 2x 16x 5y 4y 8z 10z Three Kinds of Polynomials A monomial is a polynomial with one term such as 5b6. A binomial is a polynomial with two unlike terms such as 2x 4y. A trinomial is a polynomial with three unlike terms such asy3 8z - 2. 73 ALGEBRA REVIEW Now combine like terms 14x 9y 18z To multiply monomials multiply their coefficients and multiply like variables by adding their exponents. Example -4a3b 6a2b3 -4 6 a3 a2 b b3 -24a5b4 To divide monomials divide their coefficients and divide like variables by subtracting their exponents. Example 10x5 _ 40 V xiv yL - 2x5 15x4y2 15 x4 y2 3 To multiply a polynomial by a monomial multiply each term of the polynomial by the monomial and add the products. Example 8x 12x 3y 9 Distribute. 8x 12x 8x 3y 8x 9 Simplify. 96x2 24xy 72x To divide a polynomial by a monomial divide each term of the polynomial by the monomial and add the quotients. Example 6x - I8 . 42 6x 18 . 42 6 6 6 6 x 3y 7 Practice Question Which of the following is the solution to 18x3 a. 1 18x11y9 b. 247 c. 42x11y9 d. e. 4 Answer d. To find the quotient 18x8y5 24x3y4 3x8 - 3y5 - 4 4 3x5y1 4 3x5y - 4 Divide the coefficients and subtract the exponents. 74 --------------------------------------- ALGEBRA REVIEW .