How can [tex]f(x) = 6x^2 + 5x - 6[/tex] be factored to reveal the zeros of the function it defines?

6 x^2+5 x-6 Factor the quadratic 6 x^2+5 x-6. The coefficient of x^2 is 6 and the constant term is -6. The product of 6 and -6 is -36. The factors of -36 which sum to 5 are -4 and 9. So 6 x^2+5 x-6 = 6 x^2+9 x-4 x-6 = 3 (3 x-2)+2 x (3 x-2): 3 (3 x-2)+2 x (3 x-2) Factor 3 x-2 from 3 (3 x-2)+2 x (3 x-2): Answer: | | (3 x-2) (2 x+3) Zeros: 2/3 , -3/2

Answered by beshoyhenin | 2024-06-10

The quadratic function f ( x ) = 6 x 2 + 5 x − 6 can be factored into ( 2 x + 3 ) ( 3 x − 2 ) . The zeros of the function are found at x = − 2 3 ​ and x = 3 2 ​ . This step-by-step breakdown reveals the process of factoring and identifying the zeros of the function.
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Answered by beshoyhenin | 2024-10-29