3x² + 8x + 4 First, i divide the equation into two parenthesis, so that the first parts of both multiply to make the first term, 3x². 3x * x = 3x² (3x + )(x + ) Then I find two numbers that multiply to make 4, which are 1 and 4, or 2 and 2. Our options are: (3x + 1)(x + 4) (3x + 4)(x + 1) (3x + 2)(3x +2)
To figure out which one to use, I'm just going to FOIL them all. (3x + 1)(x + 4) = 3x² + 1x + 12x + 4 = 3x² + 13x + 4 (3x + 4)(x + 1) = 3x² + 4x + 3x + 4 = 3x² + 7x + 4 (3x + 2)(x +2) = 3x² + 2x + 6x + 4 = 3x² + 8x + 4
The factored form is: (3x + 2)(x + 2)
To solve for the roots ( where the graph crosses the x axis, where y = 0) we set the equation equal to 0:
(3x + 2)(x + 2) = 0 The zero product property says that anything times 0 is 0, so we set each individual part equal to 0 and solve for the two roots.
