Question

1. $15x^4 - 125x^3 + 210x^2$

Explanation:

Step1: Factor out the greatest common factor (GCF)

The GCF of \(15x^{4}\), \(-125x^{3}\), and \(210x^{2}\) is \(5x^{2}\).

$$15x^{4}-125x^{3}+210x^{2}=5x^{2}(3x^{2}-25x + 42)$$

Step2: Factor the quadratic trinomial

We need to factor \(3x^{2}-25x + 42\). We look for two numbers that multiply to \(3\times42 = 126\) and add up to \(-25\). The numbers are \(-18\) and \(-7\).

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Step3: Combine the factors

Putting it all together, we have:

$$15x^{4}-125x^{3}+210x^{2}=5x^{2}(3x - 7)(x - 6)$$

Answer:

\(5x^{2}(3x - 7)(x - 6)\)