Answer:
C. 3x + 8
Step-by-step explanation:
We have the quadratic expression \(12x^2+29x-8\).
Equating the expression to 0, we get the equation, \(12x^2+29x-8=0\).
Now, we know the solution of the quadratic equation \(ax^2+bx+c=0\) is given by \(x=\frac{-b\pm \sqrt{x^{2}-4ac}}{2a}\)
As, we have,
a= 12, b= 29 and c= -8.
The solution is given by,
\(x=\frac{-29\pm \sqrt{29^{2}-4\times 12\times (-8)}}{2\times 12}\)
i.e. \(x=\frac{-29\pm \sqrt{841+384}}{24}\)
i.e. \(x=\frac{-29\pm \sqrt{1225}}{24}\)
i.e. \(x=\frac{-29\pm 35}{24}\)
i.e. \(x=\frac{-29+35}}{24}\) and \(x=\frac{-29-35}{24}\)
i.e. \(x=\frac{6}}{24}\) and \(x=\frac{-64}{24}\)
i.e. \(x=\frac{1}}{4}\) and \(x=\frac{-8}{3}\)
So, the factors of the expression \(12x^2+29x-8\) are (4x-1) and (3x+8).
Thus, according to the options, the expression which is factor of the given equation is 3x + 8.
