Question

question
factor completely:
$2x^3 - 34x^2 + 140x$
answer attempt 1 out of 2

Explanation:

Step1: Factor out GCF

The greatest common factor (GCF) of \(2x^3\), \(-34x^2\), and \(140x\) is \(2x\). Factor it out:
\(2x(x^2 - 17x + 70)\)

Step2: Factor quadratic

Factor \(x^2 - 17x + 70\). Find two numbers that multiply to \(70\) and add to \(-17\) (both negative: \(-7\) and \(-10\)):
\(x^2 - 17x + 70 = (x - 7)(x - 10)\)

Step3: Combine factors

Substitute the factored quadratic back:
\(2x(x - 7)(x - 10)\)

Answer:

\(2x(x - 7)(x - 10)\)