To Factor ax 2 + bx + c by reversing FOIL Example: Factor: 3x 2  14x  5 (3x  5)(x + 1) = 3x 2 + 3x  5x  5 = 3x 2  2x  5 (3x  1)(x + 5) = 3x 2.

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Presentation transcript:

To Factor ax 2 + bx + c by reversing FOIL

Example: Factor: 3x 2  14x  5 (3x  5)(x + 1) = 3x 2 + 3x  5x  5 = 3x 2  2x  5 (3x  1)(x + 5) = 3x x  x  5 = 3x x  5 (3x + 5)(x  1) = 3x 2  3x + 5x  5 = 3x 2 + 2x  5 (3x + 1)(x  5) = 3x 2  15x + x  5 = 3x 2  14x  5 Wrong middle term Correct middle term! Example: Factor: 18x 3  141x 2  24x Example: Factor 14x + 5  3x 2

Equations and Functions We now use our new factoring skills to solve a polynomial equation. We factor a polynomial expression and use the principle of zero products to solve the equation. Example Solve: 2x 5 = 7x 4 – 3x 3. Solution—Algebraic Set the equation equal to zero and factor. 2x 5 – 7x 4 + 3x 3 = 0 x 3 (2x – 1)(x – 3) = 0 x 3 = 0 or 2x – 1 = 0 or x – 3 = 0 x = 0 or x = ½ or x = 3 The solutions are x = 0, x = ½ or x = 3.

Graphical Solution Enter into the y-editor y1 = 2*x ^ 5– (7*x ^ 4 – 3*x ^ 3) Using the ZERO option of the CALC menu we get. Hard to see the zeros. We must change the window size. Still a little hard to see the zeros. Three zeros. 123 The zeros are x = 0, 0.5, or 3

Example Find the domain of f if f (x) = Solution The domain of f is the set of all values for which the function is a real number. Since division by 0 is undefined, we exclude any x-value for which the denominator is 0. x 2 + 2x – 8 = 0 (x – 2)(x + 4) = 0 x – 2 = 0 or x + 4 = 0 x = 2 or x = –4 These are the values to exclude. The domain of f is {x| x  2 or x   4}.

Examples