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

Hello I need help with a problem “In the following exercises, factor completely”-example-1

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Answer


\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))

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