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ExponentsPolynomials

Blitzer Introductory Algebra for College Students 5th ed Chapter 6

QuestionAnswer
How do you subtract polynomials? To subtract two polynomials, add the first polymonial and the opposite of the polynomial being subtracted.
What is a polynomial? A polynomial is a single term or the sum of two or more terms containing variables with whole-number exponents.
What is the standard form of a polynomial? It is customary to write the terms in the order of descending powers of the variables.
How do you multiply fractions? 1. Multiply the top numbers (the numerators). 2. Multiply the bottom numbers (the denominators). 3. Simplify the fraction if needed.
What is the degree of a polymonial? The degree of a polynomial is the greatest degree of all terms of the polymonial.
How do you add polynomials? Polynomials are added by combining like terms.
Multiplying polynomials: What is the product rule? The Product Rule says: When multiplying exponential expressions with the same base, add the exponents. Use the sum as the exponent of the common base.
Multiplying polynomials: What is the power rule? The Power Rule says: When an exponential expression is raised to a power, multiply the exponents. Place the product of the exponents on the base and remove the parentheses.
Multiplying polynomials: What is the products-to-powers rule? The Products-to-Powers Rule says: When a product is raised to a power, raise each factor to the power.
How do you multiply a monomial and a polynomial that is not a monomial? To multiply a monomial and a polynomial, use the distributive property to multiply each term of the polynomial by the monomial.
How do you multiply polynomials when neither is a monomial? Multiply each term of one polynomial by each term of the other polynomial. Then combine like terms.
How do you find the product of two binomials?Name two methods. 1. Double distribute.2. FOIL
What is the double distribute method of finding the product of two binomials? Simply distribute each term in the first binomial through the second binomial. This method always works.
What is the FOIL method of finding the product of two binomials? F = the product of the FIRST terms in each binomial, O = the product of the OUTSIDE terms, I = the product of the INSIDE terms, and L = the product of the LAST or second terms in each binomial.
What is the shortcut to finding the product of the sum and difference of two identical terms? The product of the sum and the difference of the same two terms is the square of the first term minus the square of the second term.
What is the square of a binomial sum? The square of a binomial sum is the first term squared PLUS 2 times the product of the terms plus the last term squared.
What is the square of a binomial difference? The square of a binomial difference is the first term ssquared MINUS 2 times the product of the terms plus the last term squared.
What is the FOIL formula? (A+B)(C+D) = AC + AD + BC + BD
What is the "Sum and Difference of Two Terms" formula? (A+B)(A-B) = A squared - B squared
What are the formulas for the "Square of a Binomial"? SUM(A + B)squared = A squared + 2AB + B squaredDIFFERENCE (A + B) squared = A squared - 2AB + B squared
Created by: IdleAwhile