To factor the given polynomial [tex]\( 6xy - 8x^2 \)[/tex], follow these steps:
1. Identify common factors:
Both terms in the polynomial [tex]\( 6xy \)[/tex] and [tex]\( -8x^2 \)[/tex] share a common factor. Here, the greatest common factor (GCF) is [tex]\( 2x \)[/tex].
2. Factor out the GCF:
Factor [tex]\( 2x \)[/tex] out of each term in the polynomial:
[tex]\[
6xy - 8x^2 = 2x(3y) - 2x(4x)
\][/tex]
After factoring out [tex]\( 2x \)[/tex], we get:
[tex]\[
= 2x (3y - 4x)
\][/tex]
3. Rewrite the polynomial in its complete factored form:
Thus, the complete factored form of the polynomial [tex]\( 6xy - 8x^2 \)[/tex] is:
[tex]\[
= -2x(4x - 3y)
\][/tex]
Here, the factor of [tex]\(-1\)[/tex] is included to ensure the expression matches our ultimate goal.
So, the complete factored form of the polynomial [tex]\( 6xy - 8x^2 \)[/tex] is:
[tex]\[
-2x(4x - 3y)
\][/tex]
This is the correct, fully factored expression.
