College Algebra (Abridged)

It can be seen that the two equations form parallel lines with each other and thus have no points of intersection. 1.9 Polynomials Up to this point, we have simplified and solved the linear equations whose variables have the power of 1. We shall now discuss how to factor, simplify, and solve linear equations using polynomials. Polynomials are defined as those mathematical expressions that take the following form: ( ) = + −1 −1 + −2 −2 + ⋯ + 1 + 0 For example: ( ) = 4 3 − 6 2 + 9 + 12 In this case, 3 = 4, 2 = − 6, 1 = 9 and 0 = 12 The values of , −1 , −2 , …, 1 and 0 are known as the coefficients of polynomials and the power of x determines the degree of ( ) , also known as the leading term. The equation with a maximum of two degrees of the unknown variable is known as a quadratic equation. Addition and subtraction of polynomials are possible only between like terms --those terms which have the same variable(s) raised to the same exponent. For instance, we are given these two polynomials: ( ) = 4 3 − 6 2 + 9 + 12

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