Question

1. which expression is a factor of $5x^2 - 30x - 80$?

options:

• $x - 4$
• $x - 8$
• $x + 8$
• $x + 4$

Explanation:

Step1: Factor out the greatest common factor

First, we can factor out a 5 from the quadratic expression \(5x^{2}-30x - 80\). So we have \(5(x^{2}-6x - 16)\).

Step2: Factor the quadratic inside the parentheses

We need to factor \(x^{2}-6x - 16\). We look for two numbers that multiply to - 16 and add up to - 6. The numbers are - 8 and 2 because \((-8)\times2=-16\) and \(-8 + 2=-6\). So we can write \(x^{2}-6x - 16=(x - 8)(x+2)\).

Step3: Write the fully factored form

Putting it all together, the factored form of \(5x^{2}-30x - 80\) is \(5(x - 8)(x + 2)\). So one of the factors is \(x-8\).

Answer:

B. \(x - 8\)