Let's proceed with matching each expression to its factored form step-by-step:
1. Expression: [tex]\( 56x^3 - 7x^2 \)[/tex]
- Considering the factored forms given, none of the provided options correspond to the factored form of this expression.
- Therefore, there is no match for this expression in the provided factored forms.
2. Expression: [tex]\( 18x^2 + 27x - 9 \)[/tex]
- This expression can be factored as [tex]\( 9(2x^2 + 3x - 1) \)[/tex].
- Thus, it matches factored form [tex]\( 9(2x^2 + 3x - 1) \)[/tex].
3. Expression: [tex]\( 4x^2 + 32 \)[/tex]
- This expression can be factored as [tex]\( 4(x^2 + 8) \)[/tex].
- Thus, it matches factored form [tex]\( 4(x^2 + 8) \)[/tex].
4. Expression: [tex]\( 6x^4 - 4x^2 + 14x \)[/tex]
- Considering the factored forms given, none of the provided options correspond to the factored form of this expression.
- Therefore, there is no match for this expression in the provided factored forms.
To summarize:
- Expression 1: [tex]\( 56x^3 - 7x^2 \)[/tex] has no corresponding factored form provided.
- Expression 2: [tex]\( 18x^2 + 27x - 9 \)[/tex] matches with [tex]\( 9(2x^2 + 3x - 1) \)[/tex].
- Expression 3: [tex]\( 4x^2 + 32 \)[/tex] matches with [tex]\( 4(x^2 + 8) \)[/tex].
- Expression 4: [tex]\( 6x^4 - 4x^2 + 14x \)[/tex] has no corresponding factored form provided.
Therefore, the final matching is:
[tex]\[
\begin{aligned}
&1. &\text{No match} \\
&2. &9(2x^2 + 3x - 1) \\
&3. &4(x^2 + 8) \\
&4. &\text{No match} \\
\end{aligned}
\][/tex]
