Question

factor completely. 15t³ - 10t² + 3t - 2

Explanation:

Step1: Group the terms

We can group the first two terms and the last two terms together:
\((15t^{3}-10t^{2})+(3t - 2)\)

Step2: Factor out the GCF from each group

For the first group \(15t^{3}-10t^{2}\), the greatest common factor (GCF) is \(5t^{2}\). Factoring it out gives:
\(5t^{2}(3t - 2)\)
For the second group \(3t - 2\), the GCF is \(1\), so it remains as \(1(3t - 2)\)

Step3: Factor out the common binomial factor

Now we can see that both terms have a common factor of \((3t - 2)\). Factoring that out gives:
\((3t - 2)(5t^{2}+1)\)

Answer:

\((3t - 2)(5t^{2}+1)\)