How to Identify the Coefficient of Each Term of the Polynomial

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Polynomials are expressions that contain one or more terms. A term consists of a constant that multiplies one or more variables and is referred to as the coefficient. For example, in the polynomial term 2x, the coefficient is 2 and the variable is x. The coefficient of the term with the highest degree variable is known as the leading coefficient, which cannot be equal to zero. A term without a variable is a constant and thus has no coefficient.

  • Combine the like terms in the polynomial. These are terms with the same variables in the same degrees. For example, in the polynomial 2x^3 + 4x^2 + 3x + 3x^2 + 10, the terms 4x^2 and 3x^2 are like terms because the variables are of degree two in both. Combine the like terms to get 2x^3 + 7x^2 + 3x + 10.

  • Identify the coefficient in each term. It is the constant in front of the variables. In the example, the coefficients are 2, 7 and 3 for 2x^3, 7x^2 and 3x, respectively. Note that the fourth term, 10, is a constant.

  • Use multicolored and differently-shaped algebra tiles to identify the coefficients of polynomial terms. These tiles help you visualize algebra problems. For example, use green cube, square, narrow rectangle and short rectangle tiles to represent x^3, x^2, x and a constant term, respectively. You could use green tiles for positive terms and blue tiles for negative terms. Count the number of cubes, squares and narrow rectangles to identify the coefficients for the respective terms. In the example, you will have 2 green cube tiles, 7 green square tiles, 3 green narrow rectangle tiles and 10 green short rectangle tiles to represent the polynomial. Thus, the coefficients are 2, 7 and 3 for the first, second and third terms, respectively.

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