Question

What is the expression in factored form?9x^2-4

Answer 1

To find the factored form of a polynomial, like:

`9x^2-4`

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:

`9x^2-4=9(x-x_1)(x-x_2)`

To find the zeros, x₁ and x₂, we can equalize the polynomial to zero and solve for x:

`\begin{gathered} 9x^2-4=0 \\ 9x^2=4 \\ x^2=(4)/(9) \\ x=\pm\sqrt[]{(4)/(9)} \\ x=\pm\frac{\sqrt[]{4}}{\sqrt[]{9}} \\ x=\pm(2)/(3) \end{gathered}`

So, the roots are +2/3 and -2/3.

The factored form is, then:

`\begin{gathered} 9(x-(2)/(3))(x-(-(2)/(3))) \\ 9(x-(2)/(3))(x+(2)/(3)) \end{gathered}`

Answer: The factored form is:

`9(x-(2)/(3))(x+(2)/(3))`