Question

Hello I need help with a problem “In the following exercises, factor completely”

Answer 1

`\begin{equation*} 8(x-(9+√(177))/(16))(x-(9-√(177))/(16)) \end{equation*}`

Explanation

Given the expression:

`8x^2-9x-3`

it has the form:

`ax^2+bx+c`

where a = 8, b = -9, and c = -3

The factored form of this type of expression is:

`ax^2+bx+c=a(x-x_1)(x-x_2)`

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:

`\begin{gathered} x_(1,2)=(-b\pm√(b^2-4ac))/(2a) \\ x_(1,2)=(9\pm√((-9)^2-4\cdot8\cdot(-3)))/(2\cdot8) \\ x_(1,2)=(9\pm√(177))/(16) \\ x_1=(9+√(177))/(16) \\ x_2=(9-√(177))/(16) \end{gathered}`

Finally, the expression completely factored is:

`8x^2-9x-3=8(x-(9+√(177))/(16))(x-(9-√(177))/(16))`