To determine the correct factor from the given expression, let's analyze it step-by-step:
Given expression:
[tex]\[ 5\left(3 x^2 + 9 x\right) - 14 \][/tex]
1. Start with the expression inside the parentheses:
[tex]\[ 3x^2 + 9x \][/tex]
2. Factor out the greatest common factor from the terms inside the parentheses. In this case, both terms inside the parentheses share a common factor of 3x:
[tex]\[ 3x( x + 3 ) \][/tex]
So the expression becomes:
[tex]\[ 5 \cdot 3x(x + 3) - 14 \][/tex]
3. Upon simplifying, the term [tex]\(5 \left(3x^2 + 9x \right)\)[/tex] can be expressed as:
[tex]\[ (5 \cdot 3x \cdot (x + 3)) - 14 \][/tex]
Notice that the term [tex]\(14\)[/tex] is isolated and not part of the factoring process inside the parentheses.
4. The expression can clearly show that the common factor involved initially was:
[tex]\[ 5 \][/tex]
So, determining the overall expression, the correct factor that was taken out from the terms is indeed 5.
Therefore, the correct answer is:
[tex]\[
\boxed{5}
\][/tex]
