SOLUTION: factoring trinomials by grouping 60p^4+81p^3+27p^2

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Question 57331: factoring trinomials by grouping
60p^4+81p^3+27p^2
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
factoring trinomials by grouping
60p%5E4%2B81p%5E3%2B27p%5E2 Factor out the GCF 3p^2
3p%5E2%2820p%5E2%2B27p%2B9%29
We need to replace the middle term, 27p, of the trinomial with two numbers that multiply to give you (20p^2)*(9)=180p^2, but add together to get 27p.
I coudn't think of it at first so I factored 180 down to it's prime factors until I found that 12p*15P=180p^2 and 12p+15p=27p.
3p%5E2%2820p%5E2%2B12p%2B15p%2B9%29 Group the first two terms and the last two terms.
3p%5E2%28%2820p%5E2%2B12p%29%2B%2815p%2B9%29%29 Factor out the GCF in each group.
3p%5E2%284p%285p%2B3%29%2B3%285p%2B3%29%29 Both now have a factor of (5p+3) factor it out.
3p%5E2%285p%2B3%29%284p%2B3%29
Happy Calculating!!!