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Factor the polynomial.

[tex]\[ 6d^2 - 21d \][/tex]

Sagot :

GinnyAnsweridn
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]
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