^{2}- 46X + 42 = 2 ( 6X

^{2 }- 23X + 21)

^{2}- 9X - 14 X + 21) = 2 [ 3X( 2X -3) - 7( 2X -3) ] = 2( 2X -3 ) ( 3X -7 )

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

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Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...

12 X^{2} - 46X + 42 = 2 ( 6X^{2 }- 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 X^{2} - 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.

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!

Ryan S. | Mathematics and StatisticsMathematics and Statistics

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).

Let us look at this trinomial:

12x^{2}-46x+42;

The best way to factor it is to use a quadratic formula. If you know the roots of the equation 12x^{2}-46x+42=0, then it can be factored as follows:

12x^{2}-46x+42=12(x-x_{1})(x-x_{2}), where x_{1} and x_{2} are the roots.

Quadratic formula gives us:

x_{1,2}=[46±√(46^{2}-12*42*4)]/24;

x_{1,2}=(46±√100)/24=(46±10)/24

x_{1}=3/2;

x_{2}=7/3;

Thus, we have:

12x^{2}-46x+42=12(x-3/2)(x-7/3)=2*(2x-3)(3x-7)

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## Comments

^{2}- 23x + 21] and then you just multiply each term in the parentheses by 2 to get 12x^{2}- 46x + 42.