Question

7x² - 49x + 70

Explanation:

Step1: Factor out the GCF

The greatest common factor (GCF) of \(7x^2\), \(-49x\), and \(70\) is \(7\). So we factor out \(7\):
\(7(x^2 - 7x + 10)\)

Step2: Factor the quadratic

We need to factor \(x^2 - 7x + 10\). We look for two numbers that multiply to \(10\) and add up to \(-7\). The numbers are \(-2\) and \(-5\) because \((-2)\times(-5)=10\) and \((-2)+(-5)=-7\). So we can write:
\(x^2 - 7x + 10=(x - 2)(x - 5)\)

Step3: Combine the factors

Putting it all together, the factored form of the original expression is:
\(7(x - 2)(x - 5)\)

Answer:

\(7(x - 2)(x - 5)\)