Question

solve the following equation by factoring.
$x^2 - 17x = 0$
rewrite the equation in a completely factored form.
$\square = 0$
(type your answer in factored form.)
the solution set is $\\{\square\\}$.
(simplify your answer. use a comma to separate answers as needed.)

Explanation:

Step1: Factor out common term

The equation is \(x^2 - 17x = 0\). Both terms have a common factor of \(x\). Factoring out \(x\), we get \(x(x - 17)=0\).

Step2: Solve for x

Using the zero - product property, if \(ab = 0\), then either \(a = 0\) or \(b = 0\). So, for \(x(x - 17)=0\), we have two cases:

• Case 1: \(x=0\)
• Case 2: \(x - 17=0\), which gives \(x = 17\)

Answer:

The factored form is \(x(x - 17)=0\). The solution set is \(\{0,17\}\)