# Identifying Terms, Factors, and Coefficients

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Identifying Terms, Factors, and Coefficients

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 ax2 + 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

5.1.1: Identifying Terms, Factors, and Coefficients
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

5.1.1: Identifying Terms, Factors, and Coefficients
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. 5x2 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 x2 + 6x – 2 is an example of a trinomial. 5.1.1: Identifying Terms, Factors, and Coefficients

5.1.1: Identifying Terms, Factors, and Coefficients
Practice Identify each term, coefficient, and constant of 6(x – 1) – x(3 – 2x) Classify the expression as a monomial, binomial, or trinomial. Determine whether it is a quadratic expression. 5.1.1: Identifying Terms, Factors, and Coefficients

Simplify the expression.
The expression can be simplified by following the order of operations and combining like terms. 6(x – 1) – x(3 – 2x) + 12 Original expression 6x – 6 – x(3 – 2x) + 12 Distribute 6 over x – 1. 6x – 6 – 3x + 2x2 + 12 Distribute –x over 3 – 2x. 3x x2 Combine like terms: 6x and –3x; –6 and 12. 2x2 + 3x + 6 Rearrange terms so the powers are in descending order. 5.1.1: Identifying Terms, Factors, and Coefficients

5.1.1: Identifying Terms, Factors, and Coefficients
Solution Identify all terms. There are three terms in the expression: 2x2, 3x, and 6. Identify all coefficients. The number multiplied by a variable in the term 2x2 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

5.1.1: Identifying Terms, Factors, and Coefficients
Solution, continued Identify all coefficients. The number multiplied by a variable in the term 2x2 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

5.1.1: Identifying Terms, Factors, and Coefficients
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 ax2 + bx + c, where a = 2, b = 3, and c = 6. 5.1.1: Identifying Terms, Factors, and Coefficients

5.1.1: Identifying Terms, Factors, and Coefficients
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 2x2, 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

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