Math problem

Question

2x^2+3x-5

(X+5)(2x-1)

 

i am stuck on finding out where the error is made a solving it. 

Answer 1

Hello Natasha

 

I suppose your answer is (X+5) (2X-1)

 

However, if you check your answer you can realize that is not a match with the original equation:

 

(X+5) (2X-1)= 2X² - X +10X - 5  =>  2X² + 9X - 5    and this this different to 2X² + 3X - 5 (the original).

 

If you apply the quadratic equation you can solve the problem:

 

X= -b +/- √¯(b² - 4 a c)                     in the equation with this form:   aX² + bX + c

     ------------------------  

                 2 a

 

Applying the above:  a= 2    b= 3  &  c= -5   in the original equation

 

X = -3 +/- √¯(3² - (4 x 2 x (-5)))      - 3+/- √¯(9 + 40)     - 3 +/-  7

      ---------------------------------  =  ------------------- =   -------------

                     2 x 2                                       4                        4

 

 

So X has two values:

 

X = (-3-7)/4  =  - 5/2

 

and

 

X = (-3+7)/4 =      1

 

Then the answer is:  (X + 5/2) (X - 1)

 

Of course, you can corroborate it:

 

(X + 5/2) (X - 1) = X² - X + 5/2 X -5/2     =>  X² + 3/2 X  - 5/2

 

If you want to simplify, you can multiply all terms by 2:

 

2X² + (3/2x2) X - (5/2 x 2)   =>   2X² + 3X -5 (the original equation)

 

 

 

 

 

 

Answer 2

2x² + 3x- 5

 

Use the ac method, where a = 2 , b = 3, and c = -5:

 

a*c = -10

 

We want two factors that multiply to -10 and add to 3.  Answer = 5 and -2

• 5*(-2) = -10
• 5 + -2 = 3

 

Now factor by grouping:

 

2x² + 3x- 5

2x² -2x + 5x - 5

2x(x-1) + 5(x-1)

 

(2x+5)(x-1)