Polynomial Functions and Adding and Subtracting Polynomials 5.2 Polynomial Functions and Adding and Subtracting Polynomials

Polynomial Vocabulary Term – a number or a product of a number and variables raised to powers Coefficient – numerical factor of a term Constant – term which is only a number Polynomial is a sum of terms involving variables raised to a whole number exponent, with no variables appearing in any denominator.

Polynomial Vocabulary In the polynomial 7x5 + x2y2 – 4xy + 7, there are ____terms: The coefficient of term 7x5 is ____, of term x2y2 is ____, of term – 4xy is ____ and of term 7 is ____. _____ is a constant term.

Types of Polynomials Monomial is a polynomial with one term. Binomial is a polynomial with two terms. Trinomial is a polynomial with three terms.

Degrees Degree of a term To find the degree, take the _______ of the exponents on the variables contained in the term. Degree of a constant is _____. Degree of the term 5a4b3c is ____ (remember that c can be written as c1). Degree of a polynomial To find the degree, take the largest degree of any term of the polynomial. Degree of 9x3 – 4x2 + 7 is 3.

Example If P(x) = 3x2 – 2x – 5, find the following, a. P(1) b. P(–2)

Combining Like Terms Example: ______________are terms that contain exactly the same variables raised to exactly the same powers. Warning! Only like terms can be combined through addition and subtraction. Example: Combine like terms to simplify. x2y + xy – y + 10x2y – 2y + xy

Adding Polynomials Adding Polynomials To add polynomials, combine all the like terms. Example: Add. (3x – 8) + (4x2 – 3x +3)

Subtracting Polynomials To subtract two polynomials, change the signs of the terms of the polynomial being subtracted and then add. Example: a) Subtract 4 – (– y – 4) b) Simplify (– a2 + 1) – (a2 – 3) + (5a2 – 6a + 7)