Answer :
Answer
[tex]\begin{equation*} 8(x-\frac{9+\sqrt{177}}{16})(x-\frac{9-\sqrt{177}}{16}) \end{equation*}[/tex]Step-by-step explanation
Given the expression:
[tex]8x^2-9x-3[/tex]it has the form:
[tex]ax^2+bx+c[/tex]where a = 8, b = -9, and c = -3
The factored form of this type of expression is:
[tex]ax^2+bx+c=a(x-x_1)(x-x_2)[/tex]where x₁ and x₂ are the zeros of the function.
To find the zeros of this expression we can use the quadratic formula, as follows:
[tex]\begin{gathered} x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ x_{1,2}=\frac{9\pm\sqrt{(-9)^2-4\cdot8\cdot(-3)}}{2\cdot8} \\ x_{1,2}=\frac{9\pm\sqrt{177}}{16} \\ x_1=\frac{9+\sqrt{177}}{16} \\ x_2=\frac{9-\sqrt{177}}{16} \end{gathered}[/tex]Finally, the expression completely factored is:
[tex]8x^2-9x-3=8(x-\frac{9+\sqrt{177}}{16})(x-\frac{9-\sqrt{177}}{16})[/tex]