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 August 4th, 2013, 07:49 AM #1 Newbie   Joined: Jul 2013 Posts: 21 Thanks: 0 How to factor this polynomial How do you factor this: 8(3a-7)^2+2(3a-7)-45 ? I tried Mathway and the answer was this: 3(2a-3)(12a-37) But I have no idea how it came up with that. Help me please. Thank you.
 August 4th, 2013, 08:00 AM #2 Senior Member   Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11 Re: How to factor this polynomial $8(3a-7)^2+2(3a-7)-45$ substitue $t=3a-7$ to get $8t^2+2t-45$ solve for t: $D=4+180*8=1444=38^2 t_{1,2}= \frac {(-1+-19)}{8} so 8t^2+2t-45=8(t-9/4)(t+5/2)=(4t-9)(2t+5)$ fill in $t=3a-7$ $(12a-37)(6a-9)$
 August 4th, 2013, 12:02 PM #3 Member   Joined: Jul 2013 Posts: 58 Thanks: 0 Re: How to factor this polynomial hi , Gelatine.. If the situation were something like... 8(3a-7)^2 + 2(3a-7), then, can I calculate this like .. 8+2 , (3a-7) + ( 3a-7) ? so it will be 10{(3a-7)+(3a-7)} ?
 August 4th, 2013, 12:12 PM #4 Senior Member   Joined: Jul 2013 From: Croatia Posts: 180 Thanks: 11 Re: How to factor this polynomial No, since you have square of (3a-7) $8(3a-7)^2 + 2(3a-7)=8(3a-7)(3a-7)+2(3a-7)=(3a-7)[8(3a-7)+2]=(3a-7)(24a-54)=6(3a-7)(4a-9)$

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