Slide 1

Slide 2 Identifying Terms, Factors, and Coefficients ~adapted from walch education Slide 3 Quadratic Expressions A quadratic expression is an expression where the highest power of the variable is the second power. A quadratic expression can be written in the form ax 2 + bx + c, where x is the variable, and a, b, and c are constants. Both b and c can be any number, but a cannot be equal to 0 because quadratic expressions must contain a squared term. 5.1.1: Identifying Terms, Factors, and Coefficients 2 Slide 4 Key Concepts A term is a number, a variable, or the product of a number and variable(s). A factor is one of two or more numbers or expressions that when multiplied produce a given product. The number multiplied by a variable in an algebraic expression is called a coefficient. A term that does not contain a variable is called a constant term because the value of the term does not change. 5.1.1: Identifying Terms, Factors, and Coefficients 3 Slide 5 Polynomials A polynomial is a monomial or the sum of monomials. A polynomial can have any number of terms. A monomial is a number, a variable, or the product of a number and variable(s). We can also think of a monomial as an expression containing only one term. 5x 2 is an example of a monomial. A binomial is a polynomial with two terms. 6x + 9 is an example of a binomial. A trinomial is a polynomial with three terms. 4x 2 + 6x 2 is an example of a trinomial. 5.1.1: Identifying Terms, Factors, and Coefficients 4 Slide 6 Practice Identify each term, coefficient, and constant of 6(x 1) x(3 2x) + 12. Classify the expression as a monomial, binomial, or trinomial. Determine whether it is a quadratic expression. 5.1.1: Identifying Terms, Factors, and Coefficients 5 Slide 7 Simplify the expression. The expression can be simplified by following the order of operations and combining like terms. 5.1.1: Identifying Terms, Factors, and Coefficients 6 6(x 1) x(3 2x) + 12Original expression 6x 6 x(3 2x) + 12Distribute 6 over x 1. 6x 6 3x + 2x 2 + 12Distribute x over 3 2x. 3x + 6 + 2x 2 Combine like terms: 6x and 3x; 6 and 12. 2x 2 + 3x + 6 Rearrange terms so the powers are in descending order. Slide 8 Solution Identify all terms. There are three terms in the expression: 2x 2, 3x, and 6. Identify all coefficients. The number multiplied by a variable in the term 2x 2 is 2; the number multiplied by a variable in the term 3x is 3; therefore, the coefficients are 2 and 3. 5.1.1: Identifying Terms, Factors, and Coefficients 7 Slide 9 Solution, continued Identify all coefficients. The number multiplied by a variable in the term 2x 2 is 2; the number multiplied by a variable in the term 3x is 3; therefore, the coefficients are 2 and 3. Identify any constants. The quantity that does not change (is not multiplied by a variable) in the expression is 6; therefore, 6 is a constant. 5.1.1: Identifying Terms, Factors, and Coefficients 8 Slide 10 Solution, continued Classify the expression as a monomial, binomial, or trinomial. The polynomial is a trinomial because it has three terms. Determine whether the expression is a quadratic expression. It is a quadratic expression because it can be written in the form ax 2 + bx + c, where a = 2, b = 3, and c = 6. 5.1.1: Identifying Terms, Factors, and Coefficients 9 Slide 11 Your Turn A fence surrounds a park in the shape of a pentagon. The side lengths of the park in feet are given by the expressions 2x 2, 3x + 1, 3x + 2, 4x, and 5x 3. Find an expression for the perimeter of the park. Identify the terms, coefficients, and constant in your expression. Is the expression quadratic? 5.1.1: Identifying Terms, Factors, and Coefficients 10 Slide 12 THANKS FOR WATCHING!! ~ms. dambreville