SOLUTION: {{{12(p+3)^2+13(p+3)+3}}} I can't figure out how to factor this completely the answer I keep getting is p+3(12p+52) but I don't think it is right. One of the other questions I hav

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: {{{12(p+3)^2+13(p+3)+3}}} I can't figure out how to factor this completely the answer I keep getting is p+3(12p+52) but I don't think it is right. One of the other questions I hav      Log On


   

Question 131119: 12%28p%2B3%29%5E2%2B13%28p%2B3%29%2B3
I can't figure out how to factor this completely the answer I keep getting is p+3(12p+52) but I don't think it is right. One of the other questions I have is
18z%5E8-15z%5E5-18z%5E2 The answer I got to that is 3z%5E2%283z%5E4-2%29%282z%5E2%2B3%29 however i'm pretty sure that's wrong. If you could help me that would be great. Thanks so much
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Factor:
1) 12%28p%2B3%29%5E2%2B13%28p%2B3%29%2B3
To make things a little easier, you can temporarily substitute another variable, say x,for (p+3), to give you:
12x%5E2%2B13x%2B3 Factoring this trinomial, you'll get:
%283x%2B1%29%284x%2B3%29 Now you can re-substitute the (p+3) for x, to get:
%283%28p%2B3%29%2B1%29%284%28p%2B3%29%2B3%29 Now you simplify this expression.
%283p%2B9%2B1%29%284p%2B12%2B3%29
%283p%2B10%29%284p%2B15%29 ...and there you have it!
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Check:
Let's first multiply the factors using FOIL:
%283p%2B10%29%284p%2B15%29+=+12p%5E2%2B45p%2B40p%2B150 = 12p%5E2%2B85p%2B150
Now we'll expand the given trinomial that you were asked to factor:
12%28p%2B3%29%5E2%2B13%28p%2B3%29%2B3+=+12%28p%5E2%2B6p%2B9%29%2B13%28p%2B3%29%2B3 = %2812p%5E2%2B72p%2B108%29%2B%2813p%2B39%29%2B3+=+12p%5E2%2B85p%2B150
2) Factor:
18z%5E8-15z%5E5-18z%5E2 First factor 3z%5E2
3z%5E2%286z%5E6-5z%5E3-18%29 Now, to simplify the calculations a bit, temporarily substitute x for z%5E3, but only inside the parentheses!
3z%5E2%286x%5E2-5x-6%29 Now factor the trinomial in x.
3z%5E2%283x%2B2%29%282x-3%29 Finally, you can replace the x with z%5E3
3z%5E2%283z%5E3%2B2%29%282z%5E3-3%29 ...so you were close!
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Check:
3z%5E2%283z%5E3%2B2%29%282z%5E3-3%29+=+3z%5E2%286z%5E6-9z%5E3%2B4z%5E3-6%29 = 3z%5E2%286z%5E6-5z%5E3-6%29+=+18z%5E8-15z%5E5-18z%5E2...which is exactly what you started with!