alg 2 factoring of 3x^2 - 14x + 8 need help please

[kironeko]

how can you factor 3x^2-14x+8

 

[Loren]

Re: alg 2 factorin need help please

3x^2-14x+8 = (3x - ___)(x - ___)

You fill in the blanks, remembering that their product must be 8 and when you check by multiplying the two binomials together the cross product must be -14x.

 

[masters]

Here's something to try:

$\displaystyle 3x^2-14x+8$

Multiply leading coefficient times constant:

$\displaystyle 3\times8=24$

Now find two factors of 24 that add up to -14. That'd be -12 and -2.
Replace the middle term with $\displaystyle -12x-2x$

$\displaystyle 3x^2-12x-2x+8$

Factor by grouping: $\displaystyle 3x(x-4)-2(x-4)$

$\displaystyle (3x-2)(x-4)$