I need help please!

[kellykordosky]

Trying to solve these problems and am stuck
how do you factor 3xsquared -24?
Also how do you solve for x in these problems (5x-7)(3x+4)=0 and 4xsquared +x-14=0

 

[masters]

Trying to solve these problems and am stuck
how do you factor 3xsquared -24?
Also how do you solve for x in these problems (5x-7)(3x+4)=0 and 4xsquared +x-14=0

Hi kellykordosky,

Factor: \(\displaystyle 3x^2\)-\(\displaystyle 24\)

Determine the greatest common factor (gcf) between 3 and 24. That would be 3.

Un-distribute (factor out) the 3 from the binomal 3x^2 - 24. That would be 3(x^2 - 8) Done.

Solve: (5x - 7)(3x + 4) = 0

Use the "zero product principle" that says if ab = 0, then a = 0 or b = 0. So,

5x-7=0 or 3x+4 = 0

Solve each equation.

Solve: 4x^2 + x - 14 = 0

A little more difficult, but try to follow: First, multiply the leading coefficient (4) by the constant (-14) to get (-56).

Determine 2 factors of -56 that will add up to 1 (the coefficient of the middle term). I believe if you choose +8 and -7, that would fit the bill. Their product is indeed -56 and their sum is +1.

Last thing, rewrite the quadratic equation, but this time replace the middle term with +8x - 7x. That's still 1, but you'll see why in a sec.

4x^2 + 8x - 7x -14 = 0

Group the first two terms and the last two terms.

(4x^2 + 8x) - (7x + 14) = 0 (notice the second grouping and the sign change.)

Factor out the gcf in each group.

4x(x + 2) - 7(x + 2) = 0

Now, the gcf is (x + 2) and we have, finally,

(x + 2)(4x - 7) = 0

Use the same zero product rule in the other problem to finish up.