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The table represents the multiplication of two binomials.

\begin{tabular}{|c|c|c|}
\hline & [tex]$3x$[/tex] & 5 \\
\hline[tex]$-x$[/tex] & A & B \\
\hline 2 & C & 10 \\
\hline
\end{tabular}

What is the value of [tex]$A$[/tex]?
A. [tex]$-3x$[/tex]
B. [tex]$-3x^2$[/tex]
C. [tex]$-5x$[/tex]
D. [tex]$-5x^2$[/tex]



Answer :

GinnyAnswer
To determine the value of [tex]\( A \)[/tex] in the given table, we need to understand what [tex]\( A \)[/tex] represents. The table can be interpreted as a multiplication table where each cell is the product of the binomials from the headers of the respective rows and columns.

The headers for the first row and first column are:

- The values for the first row headers are [tex]\(3x\)[/tex] and [tex]\(5\)[/tex].
- The values for the first column headers are [tex]\(-x\)[/tex] and [tex]\(2\)[/tex].

To find [tex]\( A \)[/tex], we need to multiply the elements in the header row ([tex]\(3x\)[/tex]) and the header column ([tex]\(-x\)[/tex]) that correspond to the position of [tex]\( A \)[/tex]:

The element at this position had headers [tex]\( 3x \)[/tex] horizontally and [tex]\(-x\)[/tex] vertically.

So,

[tex]\[ A = 3x \times (-x) \][/tex]

Now, let's calculate this product step-by-step:

1. Multiply the coefficients [tex]\(3\)[/tex] and [tex]\(-1\)[/tex]:
[tex]\[ 3 \times (-1) = -3 \][/tex]

2. Multiply the variable parts [tex]\(x\)[/tex] and [tex]\(x\)[/tex]:
[tex]\[ x \times x = x^2 \][/tex]

Combining these results, we get:

[tex]\[ A = -3 \times x^2 = -3x^2 \][/tex]

Therefore, the value of [tex]\( A \)[/tex] is:

[tex]\[ -3x^2 \][/tex]

So, the correct answer is [tex]\(\boxed{-3x^2}\)[/tex].

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