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B. Complete the table.

\begin{tabular}{|l|l|l|l|}
\hline
Polynomial & CMF & \begin{tabular}{c}
Quotient of \\ Polynomial and CMF
\end{tabular} & \\
\hline
[tex]$5 p^2+25 p^4$[/tex] & & & \\
\hline
[tex]$3 m-12$[/tex] & & & \\
\hline
[tex]$3 x^2-12 x y$[/tex] & & & \\
\hline
\end{tabular}

Sagot :

GinnyAnsweridn
Of course! Let's complete the table by finding the Common Monomial Factor (CMF) and the quotient of each polynomial when divided by the CMF.

### Polynomial: [tex]\( 5p^2 + 25p^4 \)[/tex]

1. Find the CMF:
- The common numerical factor between [tex]\( 5 \)[/tex] and [tex]\( 25 \)[/tex] is [tex]\( 5 \)[/tex].
- The common variable factor between [tex]\( p^2 \)[/tex] and [tex]\( p^4 \)[/tex] is [tex]\( p^2 \)[/tex].
- Therefore, the CMF is [tex]\( 5p^2 \)[/tex].

2. Find the Quotient:
- Divide each term of the polynomial by the CMF [tex]\( 5p^2 \)[/tex]:
[tex]\[ \frac{5p^2}{5p^2} = 1 \][/tex]
[tex]\[ \frac{25p^4}{5p^2} = 5p^2 \][/tex]
- Therefore, the quotient is [tex]\( 1 + 5p^2 \)[/tex].

### Polynomial: [tex]\( 3m - 12 \)[/tex]

1. Find the CMF:
- The common numerical factor between [tex]\( 3 \)[/tex] and [tex]\( -12 \)[/tex] is [tex]\( 3 \)[/tex].
- There is no common variable factor, so the CMF is just [tex]\( 3 \)[/tex].

2. Find the Quotient:
- Divide each term of the polynomial by the CMF [tex]\( 3 \)[/tex]:
[tex]\[ \frac{3m}{3} = m \][/tex]
[tex]\[ \frac{-12}{3} = -4 \][/tex]
- Therefore, the quotient is [tex]\( m - 4 \)[/tex].

### Polynomial: [tex]\( 3x^2 - 12xy \)[/tex]

1. Find the CMF:
- The common numerical factor between [tex]\( 3 \)[/tex] and [tex]\( -12 \)[/tex] is [tex]\( 3 \)[/tex].
- The common variable factor between [tex]\( x^2 \)[/tex] and [tex]\( xy \)[/tex] is [tex]\( x \)[/tex].
- Therefore, the CMF is [tex]\( 3x \)[/tex].

2. Find the Quotient:
- Divide each term of the polynomial by the CMF [tex]\( 3x \)[/tex]:
[tex]\[ \frac{3x^2}{3x} = x \][/tex]
[tex]\[ \frac{-12xy}{3x} = -4y \][/tex]
- Therefore, the quotient is [tex]\( x - 4y \)[/tex].

### Completed Table

[tex]\[ \begin{tabular}{|l|l|l|l|} \hline Polynomial & CMF & \begin{tabular}{c} Quotient of \\ Polynomial and CMF \end{tabular} & \\ \hline \( 5p^2 + 25p^4 \) & \( 5p^2 \) & \( 1 + 5p^2 \) & \\ \hline \( 3m - 12 \) & \( 3 \) & \( m - 4 \) & \\ \hline \( 3x^2 - 12xy \) & \( 3x \) & \( x - 4y \) & \\ \hline \end{tabular} \][/tex]

By identifying the CMF and performing the division for each polynomial, we obtained the quotients and completed the table.
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