I am factoring quardratic trinomials. The problem I'm working with is the following: 12x2 + -46x + 42. How do I factor it?

Question

I just need help factoring quadratic trinomials. Specifically 12x2 + -46x + 42.

Answer 1

 12 X² - 46X + 42 = 2 ( 6X² - 23X + 21) 

 

       two factor : Must be 2 numbers a,b such that    a . b = 6 ( 21) = 126    a+b =-23

 

          first we write 126 as a product of its prime factors:

 

         126 = 2 . 3 . 3 . 7 = 2 * 63 = 6 * 21= 18 * 7 = 14 * 9

 

             We find that:  -14 - 9 = -23

 

            break up -23 into -14 - 9 = -23

 

             2( 6 X² - 9X - 14 X  + 21) = 2 [ 3X( 2X -3) - 7( 2X -3) ] = 2( 2X -3 ) ( 3X -7 )

 

          This is the methods by which step by step can be followed to get the result, be able to factor.  

Answer 2

Factor a 2 out of the equation and you get 2(6x^2-23x+21).  Then factor the polynomial 2(3x-7)(2x-3).

 

Good Luck!

Answer 3

The first thing I would do is to see if I could factor out a constant. Notice that all the coefficients are even; you could at least factor out 2.

2(6x^2 - 23x + 21)

 

Let's list the possible factor pairs for 6 and 21

6= 2*3 = 6*1

21= 3*7 = 21*1

 

Notice that the middle term is negative and the final term is positive. This means that the form of the factors will be (  -  )(  -  ) because two negatives added is a negative while two negatives multiplied is a positive. Now we can try different combinations of the factors of 6 and 21 and test using FOIL.

 

(2x-7)(3x-3)= 6x^2-27x+21 Not equal to 6x^2 - 23x + 21

(2x-3)(3x-7)=6x^2 - 23x + 21 This is it!

 

So the the factors are 2(2x-3)(3x-7).

 

Answer 4

Let us look at this trinomial:

 

12x²-46x+42;

 

The best way to factor it is to use a quadratic formula. If you know the roots of the equation 12x²-46x+42=0, then it can be factored as follows:

12x²-46x+42=12(x-x₁)(x-x₂), where x₁ and x₂ are the roots.

 

Quadratic formula gives us:

 

x_1,2=[46±√(46²-12*42*4)]/24;

 

x_1,2=(46±√100)/24=(46±10)/24

x₁=3/2;

x₂=7/3;

Thus, we have:

12x²-46x+42=12(x-3/2)(x-7/3)=2*(2x-3)(3x-7)