SOLUTION: I have to factor 2p(p+1)(p-6)+16(p+1) completely. The answer is 2(p+1)(p-4)(p-2), but I don't know how to get there. PLEASE HELP!!!!!!!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I have to factor 2p(p+1)(p-6)+16(p+1) completely. The answer is 2(p+1)(p-4)(p-2), but I don't know how to get there. PLEASE HELP!!!!!!!      Log On


   

Question 115745This question is from textbook Algebra: structure and Method: book 1
: I have to factor 2p(p+1)(p-6)+16(p+1) completely. The answer is 2(p+1)(p-4)(p-2), but I don't know how to get there. PLEASE HELP!!!!!!! This question is from textbook Algebra: structure and Method: book 1

Found 2 solutions by vertciel, MathLover1:
Answer by vertciel(183) About Me  (Show Source):
You can put this solution on YOUR website!
Hello there,
2p(p + 1)(p - 6) + 16(p + 1)
=+%28p+%2B+1%29%282p%28p+-+6%29+%2B+16%29+
= +%28p+%2B+1%29%282p%5E2+-+12p+%2B+16%29+
= +%28p+%2B+1%292%28p%5E2+-+6p+%2B+8%29+
= +2%28p+%2B+1%29%28p+-+4%29%28p+-+2%29+

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
2p%28p%2B1%29%28p-6%29%2B16%28p%2B1%29………….factor out common %28p%2B1%29
%28p%2B1%29%282p%28p-6%29%2B16%29……………factor out 2
2%28p%2B1%29%28p%28p-6%29+%2B+8%29…………… multiply p%28p-6%29
2%28p%2B1%29%28p%5E2+-6p+%2B+8%29…………… factor %28p%5E2+-6p+%2B+8%29, replace -6p with -2p and -4p

28%28p%2B1%29%28p%5E2+-2p+-4p+%2B+8%29……………combine first two and second two terms
28%28p%2B1%29%28%28p%5E2+-2p%29+-%284p+-+8%29%29……………
28%28p%2B1%29%28p%28p+-2%29+-4%28p+-+2%29%29……………
common term is p-2. factor it out

2%28p%2B1%29%28p-4%29%28p-2%29….your answer