Question

course ap precalculus segment 31 - factoring: sum of cut due wed, oct 22, 2025 69 default gallery in exercises 69 - 74, factor by grouping. 69. $x^{3}-4x^{2}+5x - 20$ text math set matrix answer

Explanation:

Step1: Group the terms

Group the first two terms and the last two terms:
$$(x^{3}-4x^{2})+(5x - 20)$$

Step2: Factor out the greatest common factor from each group

For the first group \(x^{3}-4x^{2}\), the GCF is \(x^{2}\), so \(x^{2}(x - 4)\).
For the second group \(5x-20\), the GCF is \(5\), so \(5(x - 4)\).
Now we have \(x^{2}(x - 4)+5(x - 4)\)

Step3: Factor out the common binomial factor

Factor out \((x - 4)\) from the expression: \((x - 4)(x^{2}+5)\)

Answer:

\((x - 4)(x^{2}+5)\)