![]() ![]() (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression add, subtract, multiply, and divide rational expressionsĬreate equations and inequalities in one variable and use them to solve problems. Rewrite simple rational expressions in different forms write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. (+) Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle For example, the polynomial identity (x^2 + y^2 )^ 2 = (x^2 – y^ 2 )^ 2 + (2xy)^2 can be used to generate Pythagorean triples Prove polynomial identities and use them to describe numerical relationships. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x) Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication add, subtract, and multiply polynomials For example the expression 1.15^t can be rewritten as (1.15^1/12)^12t ≈ 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%ĭerive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. Use the properties of exponents to transform expressions for exponential functions. For example, see x^4 – y^ 4 as (x^2 )^ 2 – (y^2 )^ 2, thus recognizing it as a difference of squares that can be factored as (x^2 – y^ 2 )(x^2 + y^2 ).įactor a quadratic expression to reveal the zeros of the function it definesĬomplete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines Use the structure of an expression to identify ways to rewrite it. ![]() For example, interpret P(1+r)n as the product of P and a factor not depending on P Interpret complicated expressions by viewing one or more of their parts as a single entity. Interpret parts of an expression, such as terms, factors, and coefficients. Interpret expressions that represent a quantity in terms of its context. ![]()
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