Question

Which expression is a factor of 12x2 + 29x – 8?

Answer 1

$12x^2 + 29x – 8 \\ \\ 12x^2 + 32x - 3x - 8 \\ \\ 4x (3x + 8) - (3x + 8) \\ \\ (3x + 8)(4x - 1)$

The final result is: (3x + 8)(4x - 1).

Answer 2

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.