Identify Common Factor: Look for a common factor in all terms.Check if there is a greatest common factor (GCF) that can be factored out from all the terms in the polynomial 16s3−12s2+20s−15.The GCF of 16, 12, 20, and 15 is 1, so there is no common factor other than 1.
Group and Factor: Group terms to factor by grouping.Group the terms into two pairs: 16s3−12s2 and 20s−15.Now, factor out the GCF from each pair.For the first pair, the GCF is 4s2, so factor it out: 4s2(4s−3).For the second pair, the GCF is 5, so factor it out: 5(4s−3).
Write Factored Form: Write the factored form of the polynomial.Notice that both groups now have a common factor of (4s−3).Factor out (4s−3) from both groups: (4s−3)(4s2+5).
Check Factored Form: Check the factored form by expanding it to ensure it matches the original polynomial.(4s−3)(4s2+5)=4s3+20s−12s2−15.Reorder the terms to match the original polynomial: 4s3−12s2+20s−15.The expanded form matches the original polynomial, so the factoring is correct.