Question

How do you factor 27t3 + 45t2 – 3t – 5

Answer 1

The numbers after the T's are exponents. sorry i dont know how to how exponents on opeshare.

Answer 2

I'd do that by grouping:

\[27t^3+45t^2-3t-5\]\[(27t^3+45t^2) - (3t+5)\]Notice that the 5 changes sign when I move the - outside the parentheses
Now factor each group:\[9t^2(3t+5) - 1(3t+5)\]Notice that we have a common factor of \((3t+5)\) and factor that out\[(3t+5)(9t^2-1)\]Now notice that the \(9t^2-1\) is a difference of squares: \[a^2-b^2 = (a-b)(a+b)\]\[a=3t, b = 1\]\[(9t^2-1) = (3t-1)(3t+1)\]So the whole thing becomes
\[27t^3+45t^2-3t-5 = (3t+5)(3t-1)(3t+1)\]

Answer 3

How do you write exponents like that?

Answer 4

Thank you. :)

Answer 5

with \(\LaTeX\) :-)

or you can use the Equation editor button at the lower left. That's maybe easier to start. But if you see something with interesting formatting, use your mouse to select the interesting stuff, then right-click and select Show Math As->TeX commands and you'll get a popup window with the stuff needed to make it look that way. You get into \(\LaTeX\) mode by typing \ [ stuff \ ] (except without the spaces between the slashes and the [ or ])

Answer 6

Thanks i just saw that

Answer 7

so the last line of my math part was

27t^3+45t^2-3t-5 = (3t+5)(3t-1)(3t+1)

just enclosed in the \ [ \ ]

Answer 8

So is this the only easy way to do it or is there other ways?

Answer 9

what, factor, or format?