Absolutely, let's go through the steps to factor the greatest common factor of the polynomial [tex]\(-5k^2 + 20k - 30\)[/tex]:
1. Identify the Polynomial Terms:
The polynomial given is [tex]\(-5k^2 + 20k - 30\)[/tex].
2. Identify the Greatest Common Factor (GCF):
We observe that each term in the polynomial [tex]\(-5k^2\)[/tex], [tex]\(20k\)[/tex], and [tex]\(-30\)[/tex] can be divided by [tex]\(-5\)[/tex].
- Largest common factor of the coefficients (-5, 20, -30) is -5.
3. Factor Out the GCF:
- When we factor [tex]\(-5\)[/tex] out of each term, we essentially divide each term by [tex]\(-5\)[/tex]. Let's perform this operation step-by-step:
[tex]\[
-5k^2 + 20k - 30 = -5(k^2) + -5(-4k) + -5(6)
\][/tex]
Which simplifies to:
[tex]\[
-5(k^2 - 4k + 6)
\][/tex]
So, the factored form of the polynomial [tex]\(-5k^2 + 20k - 30\)[/tex] after factoring out the greatest common factor is:
[tex]\[
-5(k^2 - 4k + 6)
\][/tex]
Thus, the solution is the greatest common factor [tex]\(-5\)[/tex] and the factored polynomial is:
[tex]\[
(-5, "-5(k^2 - 4k + 6)")
\][/tex]
This demonstrates a step-by-step method to factor out the greatest common factor from the given polynomial.
