Certainly! To factor the polynomial [tex]\(6d^2 - 21d\)[/tex], let's go through the steps in detail:
1. Identify Common Factors:
First, we need to identify any common factors in the terms of the polynomial. The terms are [tex]\(6d^2\)[/tex] and [tex]\(-21d\)[/tex].
- For the coefficients: The greatest common factor (GCF) of 6 and -21 is 3.
- For the variable terms: Each term contains the variable [tex]\(d\)[/tex], and the smallest power of [tex]\(d\)[/tex] that appears in each term is [tex]\(d^1\)[/tex].
2. Factor Out the GCF:
We factor out the GCF (which is [tex]\(3d\)[/tex]) from each term in the polynomial.
[tex]\[
6d^2 - 21d = 3d(2d) - 3d(7)
\][/tex]
3. Write the Factored Form:
After factoring out [tex]\(3d\)[/tex], we combine the remaining terms inside the parentheses.
[tex]\[
6d^2 - 21d = 3d(2d - 7)
\][/tex]
Thus, the factored form of the polynomial [tex]\(6d^2 - 21d\)[/tex] is:
[tex]\[
3d(2d - 7)
\][/tex]
