I need help with finding one of the factors for x^2 - 11/12x + 1/6?

Question

I suck at fractions.


The question is Find one of the factors when x^2 - 11/12x + 1/6 is factored completely.

The answer choices are
a) x - 2/3
b) x + 1/6
c) x - 1/3
d) x - 1/2


I guessed D. but that's wrong.

Answer 1

This can be simplified by writing the equation as:
( 12x^2 - 11x + 2 ) / 12 which factors into:
[ ( 4x - 1 )( 3x - 2 ) ] / 12 which can be simplified into:
( x - 1/4 )( x - 2/3 ) so the correct answer is A.

Answer 2

Hello,

Now the factors have to multiply to be 1/6 and add to be -11/12 then they must both be negative.

Let's try the first one.

-2/3 * x (the other factor) = 1/6 then x = -1/4 now this means that (x -2/3)(x - 1/4) must equal the original polynomial.

so x^2 -2/3x - 1/4x + (-2/3)(-1/4)) does equal the original polynomial so one factor is x - 2/3 and the other is x - 1/4.

Hope This Help!!