Question

What is the GCF of the terms of 8x^3-12x^2+4x ?

Answer 1

\[\color{red}8x^3-\color{red}{12}x^2+\color{red}{4}x \] looking at this, we can not only factor out x's, because theyre common to all terms,but a 4. \[4x(2x^2-3x+1)\]

Answer 2

now we need to simplify \(\large (2x^2-3x+1)\)

Answer 3

we have to multiply the leading coefficient to the constant at the end to get a quadratic we can solve. \[\large \color{red}2x^2-3x+\color{red}1\] we get \[\large x^2-3x+2\] now we need to find 2 numbers that add to -3 and multiply to get 2.
\[\large (x-2)(x-1)\] now that we have it factored,we need to divide by 2 since we used it to multiply to the constant. \[\frac{(x-2)}{2}*\frac{(x-1)}{2}\] we find the group that can simplify the easiest, such as \[(x-\frac{2}{2})(x-\frac{1}{2})\] this can be reduced down even further.\[(x-1)(x-\frac{1}{2})\] now because we can't reduce {-1/2) easily, we multiply it to the x to get our simplified factored form.\[\large (x-1)(2x-1)\] All together we have \[\large 8x^3-12x^2+4x = 4x(2x^2-3x+1)= 4x(x+1)(2x-1)\]

Answer 4

Do you understand how I solved this?

Answer 5

not really but would the GCF be 4?

Answer 6

Not exactly, i actually showed you how to break down the entire question... in finding the exact GCF..we look at the variable and the coefficients.

we have...
x^3...x^2...x : our smallest common variable is x
8....-12...4: our smallest common coefficient is 4.

put them together you get "4x"

Answer 7

We can also find it just by partially factoring our original equation, \[\large 8x^3-12x^2+4x)= \color{red}{4x}( 2x^2-3x+1)\] the GCF is the factor we have factored out of our equation.

Answer 8

Hope that clarifies things a little more.

Answer 9

it does. thank you so much

Answer 10

Awesome :) Glad I could help.