To factor the polynomial [tex]\(10z + 25\)[/tex], let's break down the steps:
1. Identify the Greatest Common Factor (GCF): First, we need to find the GCF of the terms in the polynomial [tex]\(10z\)[/tex] and [tex]\(25\)[/tex].
The GCF of [tex]\(10z\)[/tex] and [tex]\(25\)[/tex] is [tex]\(5\)[/tex] because both 10 and 25 are divisible by 5.
2. Factor Out the GCF: We factor out the GCF from each term in the polynomial.
[tex]\[
10z + 25 = 5 \cdot 2z + 5 \cdot 5
\][/tex]
3. Rewrite the Expression: After factoring out the GCF, rewrite the polynomial:
[tex]\[
10z + 25 = 5(2z + 5)
\][/tex]
Therefore, the factored form of the polynomial [tex]\(10z + 25\)[/tex] is [tex]\(5(2z + 5)\)[/tex]. This matches the result [tex]\(5(2z + 5)\)[/tex].
