To find the factors of the polynomial [tex]\(2m^2 - 5m\)[/tex], let's proceed step by step:
1. Identify Common Factors:
First, we look for any common factors in each term of the polynomial [tex]\(2m^2 - 5m\)[/tex]. Both terms have an [tex]\(m\)[/tex] in common.
2. Factor Out the Greatest Common Factor (GCF):
Since [tex]\(m\)[/tex] is common in both terms, we factor out [tex]\(m\)[/tex] from the polynomial:
[tex]\[
2m^2 - 5m = m(2m) - m(5)
\][/tex]
When we factor [tex]\(m\)[/tex] out of [tex]\(2m^2\)[/tex], we get [tex]\(2m\)[/tex] and when we factor [tex]\(m\)[/tex] out of [tex]\(-5m\)[/tex], we get [tex]\(-5\)[/tex].
3. Express the Polynomial with the Common Factor:
After factoring out the [tex]\(m\)[/tex], we can rewrite the polynomial as:
[tex]\[
2m^2 - 5m = m(2m - 5)
\][/tex]
Thereby, the factored form of [tex]\(2m^2 - 5m\)[/tex] is:
[tex]\[
m(2m - 5)
\][/tex]
This concludes our factorization of the polynomial [tex]\(2m^2 - 5m\)[/tex].
