Question

1. what is the factor form of 4x³ - 24x² - 28x

Explanation:

Step1: Find the GCF

The terms are \(4x^3\), \(-24x^2\), and \(-28x\). The greatest common factor (GCF) of the coefficients \(4\), \(-24\), \(-28\) is \(4\), and the GCF of the variables is \(x\) (since \(x\) is the lowest power of \(x\) among the terms). So the GCF is \(4x\).

Step2: Factor out the GCF

Factor out \(4x\) from each term:
\(4x^3 - 24x^2 - 28x = 4x(x^2 - 6x - 7)\)

Step3: Factor the quadratic

Now factor the quadratic \(x^2 - 6x - 7\). We need two numbers that multiply to \(-7\) and add to \(-6\). Those numbers are \(-7\) and \(1\). So, \(x^2 - 6x - 7=(x - 7)(x + 1)\)

Step4: Combine the factors

Putting it all together, the factored form is \(4x(x - 7)(x + 1)\)

Answer:

\(4x(x - 7)(x + 1)\)