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solve by factoring

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3 Answers

3x2+17x-46=
3x2-6x+23x-46=
3x(x-2)+23(x-2)=
(3x+23)(x-2)
Dear David,
 
3x2 + 17x - 46 = (x - 2)(3x + 23)
 
If the original expression is equal to 0, then the two solutions are x = 2 and x = -7 and two thirds.
I will presume that the expression is equal to zero.
 
Solve by factoring:          3x2 + 17x - 46 = 0
 
Factor:                          (3x + 23) (x - 2) = 0
 
Set equal to zero:            3x + 23 = 0  and x - 2 = 0
 
Solve:                             x = -23/3, 2
 
Note, check by plugging the two answers into the original equation.  The -23/3 answer is a pain to check, but it did check out in the end.  It's good advanced arithmatic practice!

Comments

-23/3 = -7 2/3, because twenty-three divided by three is seven with a remainder of 2.  This is actually an important lesson.  In calculus I would often have the correct answer, but it was written in a different form than the authors wrote it in the answer section in the back of the book.  In any case, I'm just glad I was able to help.

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