Question
\( \& \quad \) Factor out the greatest common factor from the following polynomial. \[ 4 x(z+4)+(z+4) \]
Ask by Ruiz Fuentes. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The polynomial factors to \((z+4)(4x+1)\).
Solution
1. Write the original expression:
\[
4 x(z+4) + (z+4)
\]
2. Notice that \((z+4)\) is a common factor in both terms.
3. Factor out \((z+4)\):
\[
4 x(z+4) + (z+4) = (z+4)(4x + 1)
\]
4. The factored form of the polynomial is:
\[
(z+4)(4x+1)
\]
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Simplify this solution Mind Expander
The first step in factoring out the greatest common factor is to identify the common terms in each part of the polynomial. In this case, both terms \( 4x(z+4) \) and \( (z+4) \) share the common factor \( (z+4) \). By factoring \( (z+4) \) out, we rewrite the expression as: \[ (z+4)(4x + 1) \] And there you have it! The term \( (z+4) \) is the greatest common factor factored out of the original polynomial.
