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5.1 Operations with Polynomials
Recall these properties of exponents
(2k)4=
(ab)3 =
A. Simplify the expression Assume that no variable equals 0.
B. Simplify the expression . Assume that no variable equals 0.
C. Simplify the expression . Assume that no variable equals 0.
A. Simplify the expression . Assume that no variable equals 0.
Definitions
Rules of Polynomial FunctionsThere are no square roots of variables,
no fractional powers, and no variables in the denominator of any fractions
A monomial is an expression with one term.
√𝑥
Important Vocabulary
The degree of a monomial is the sum of the powers of the variable
The degree of a polynomial is the degree of the monomial with the highest degree.
C. Determine whether is a polynomial. If it is a polynomial, state the degree of the polynomial.
To simplify Polynomials, add like terms
A. Simplify (4x2 – 9x + 3) + (–2x2 – 5x – 6).
B. Simplify (2a3 + 5a – 7) – (a3 – 3a + 2).
A. Simplify (3x2 + 2x – 3) – (4x2 + x – 5).
Use distributive Property
Find –y(4y2 + 2y – 3).
Find –x(3x3 – 2x + 5).
Find (a2 + 3a – 4)(a + 2).
Find (x2 + 3x – 2)(x + 4).
Write a polynomial equation
E-SALES A small online retailer estimates that the cost, in dollars, associated with selling x units of a particular product is given by the expression0.001x
2 + 5x + 500. The revenue from sellingx units is given by 10x. Write a polynomial to represent the profits generated by the product.