Solving Equations by Factoring Chapter 5 Section 5.11

Objective Students will use factoring in solving polynomial equations

Vocabulary Polynomial equation Linear equation Quadratic equation Cubic equation Standard form

Concept Zero-Product Property For all real numbers a and b: ab = 0 if and only if a = 0 or b = 0 A product of factors is zero if and only if one or more of the factors is zero

Concept The zero-product property is true for any number of factors. You can use this property to solve certain equations.

Example Solve (x + 2)(x – 5) = 0

Example Solve 5n(n – 3)(n – 4) = 0

Concept A polynomial equation is an equation whose sides are both polynomials. Polynomial equations usually are named by the term of highest degree. If a ≠ 0: ax + b = 0 linear equation ax2 + bx + c = 0 quadratic equation ax3 + bx2 + cx + d = 0 cubic equation

Concept Many polynomial equations can be solved by factoring and then using the zero-product property. Often the first step is to transform the equation into standard form in which one side is zero. The other side should be a simplified polynomial arranged in order of decreasing degree of the variable.

Example Solve 2x2 + 5x = 12

Example Solve 18y3 + 8y + 24y2 = 0

Questions

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