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# Sec-44 - Math 1300 Section 4.4 Notes Solving Equations by...

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Math 1300 Section 4.4 Notes 1 Solving Equations by Factoring Definition: The zero-product property says that if a and b are numbers and if ab = 0, then a = 0 or b = 0 (or both). Definition: A quadratic equation is an equation that can be written ax 2 + bx + c = 0, where a , b , and c are numbers and a 0. Solving Quadratic Equations To solve a quadratic equation, we must find all possible values for x that make ax 2 + bx + c = 0. Factoring is usually a helpful way to solve quadratic equations. To use factoring, move all nonzero terms to one side of the equal sign so that the other side is zero. Then use the zero-product property. Examples: 1. Solve the equation x 2 – 5 x – 24 = 0. Only the left-hand side (LHS) of the equation has nonzero terms, so no movement of terms is necessary. Factor the LHS and use the zero-product property (ZPP): x 2 – 5 x – 24 = 0 Factor : ( x + 3)( x – 8) = 0 ZPP : x + 3 = 0 or x – 8 = 0 Solve for x : x = –3 or x = 8 2. Solve 2 x 2 + 18 x – 72 = 0 for x . All nonzero terms are on the LHS, so no movement of terms is needed. 2 x 2 + 18 x – 72 Factor : 2( x + 12)( x – 3) = 0 ZPP : x + 12 = 0 or x – 3 = 0 (Note: 2 0, so we don’t write it) Solve for x : x = –12 or x = 3 3. Solve the equation 6 x 2 – 27 x = –12. This equation has nonzero terms on both sides of the equal sign. To make it possible to solve, move the –12 to the LHS by adding 12 to both sides: 6 x 2 – 27 x + 12 = 0 Factor : 3(2 x – 1)( x – 4) = 0 ZPP : 2 x – 1 = 0 or x – 4 = 0 (Note: 3 0) Solve for x : x = ½ or x = 4 4. Solve 16 x 2 = 1. Subtract 1 from both sides

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Sec-44 - Math 1300 Section 4.4 Notes Solving Equations by...

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