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To find the factored form of a polynomial, like:
[tex]9x^2-4[/tex]We can start by finding its zeros.
This is a quadratic equation, so if both of its zeros are real, we can rewrite it as:
[tex]9x^2-4=9(x-x_1)(x-x_2)[/tex]To find the zeros, x₁ and x₂, we can equalize the polynomial to zero and solve for x:
[tex]\begin{gathered} 9x^2-4=0 \\ 9x^2=4 \\ x^2=\frac{4}{9} \\ x=\pm\sqrt[]{\frac{4}{9}} \\ x=\pm\frac{\sqrt[]{4}}{\sqrt[]{9}} \\ x=\pm\frac{2}{3} \end{gathered}[/tex]So, the roots are +2/3 and -2/3.
The factored form is, then:
[tex]\begin{gathered} 9(x-\frac{2}{3})(x-(-\frac{2}{3})) \\ 9(x-\frac{2}{3})(x+\frac{2}{3}) \end{gathered}[/tex]Answer: The factored form is:
[tex]9(x-\frac{2}{3})(x+\frac{2}{3})[/tex]