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Solving 5x^2+13x-6?

How do you solve the equation 5x2+13x-6 by factoring completely?

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1 Answer


First we need to determine which factors of 5 and 6 subtract to 13:

Factors of 5: 5 and 1

Factors of 6: 3 and 2, 6 and 1

Since we are trying to get to 13, I am focusing on the first pair that can get me greater than 13:

5*3=15, which leaves me with 1*2=2


Now I need to set this into parenthetical units:

(5x     )(x     ) I start by placing my x terms

(5x-2)(x+3) Since I need a negative 2x, I place the negative two where it multiplies by the isolated x, and this allows me to place my last factor in the remaining spot.

If you want to check your work, you can always foil out the answer, to make sure that it is the original equation.