Which equation has the same solutions as 2x^2 + x -3=0. Is it's: (2x-1)(x+3)=0 (2x+1)(x-3)=0. (2x-3)(x+1)=0. (2x+3)(x-1)=0

Question

this is for my study guide for my finale, so if you could go into full details as to how you got the answer, that would be appreciate.

Answer 1

Kelly,

A test question with one right answer among multiple choices may be answered by (1) guessing, (2) determining the correct answer, (3) checking to see whether any of the answers are correct, …

That last approach is handy if you don’t quite know how to solve the problem or if you want to save time by quickly eliminating distractors (the wrong answers).

If you remember, using FOIL, that the first term must be the product of the First terms, then check it.  Then check that the last term is the product of the Last terms (taking special notice of the sign).  Then multiply and add the outside and inside products (since that probably takes longer).  As soon as you eliminate all but one answer, you have it  (check it if you have time, or come back to check it at the end of the test).

Well, let’s try it.
   All of the answers have 2x and x so they are all still possible.
  The last terms all result in -3  (note:  these are well written distractors)
   We don’t want to be multiplying the 2x by 3 (because +- 1 will not be enough to get back to +x), so the first two equations are eliminated.

  So, now we have to get +x from either OI: (2x -3x)  or OI: (-2x + 3x).        [ from FOIL ]

        It’s (2x +3)(x-1)        check it now, or later

Answer 2

The most straightforward way to do this is to multiply each of the choices out and see which one matches the original polynomial:

 

(2x-1)(x+3)=2x(x+3)-1(x+3)=2x²+6x-x-3=2x²+5x-3, which does not match.

 

(2x+1)(x-3)=2x(x-3)+1(x-3)=2x²-6x+x-3=2x²-5x-3, which does not match

 

(2x-3)(x+1)=2x(x+1)-3(x+1)=2x²+2x-3x-3=2x²-x-3, which does not match

 

(2x+3)(x-1)=2x(x-1)+3(x-1)=2x²-2x+3x-3=2x²+x-3, which does match. This is the answer.

Answer 3

Kelly,

 

Hi!  Your quadratic equation in standard form must be factored as (2x+3)(x-1).  Why?  If you use FOIL in multiplication, the First terms 2x times x = 2x^2.  The outside terms 2x times -1 = -2x and the inside terms multiplied = 3x.  When you combine like terms, the middle term equals 'x' - the exact middle term of your beginning quadratic equation!  

Lastly, of course, your last terms of 3 times -1 =-3.  So, there you have it!! :-)

 

                                                                                                       Don M.