Question

the diagram represents the factorization of ( x^2 - 9x + 18 ). it is partially completed.
diagram: top row cells: ( x ), ( -3 ); left column cells: ( x ), ( -6 ); filled cells: ( x^2 ) (top-left), ( 18 ) (bottom-right); two cells with \?\
which two terms are missing from the diagram?
options:

• ( -x ) and ( -8x )
• ( -2x ) and ( -7x )
• ( -3x ) and ( -6x )
• ( -4x ) and ( -5x )

Explanation:

Step1: Analyze the first missing term (top right)

In the grid, the top row is \( x \) and \( -3 \), the middle row has \( x \) in the first column. To find the term in the middle row, second column, we multiply the row header (\( x \)) by the column header (\( -3 \)). So, \( x\times(-3)= -3x \).

Step2: Analyze the second missing term (bottom left)

The bottom row has \( -6 \) in the first column, and the first column header is \( x \). To find the term in the bottom row, second column, we multiply the row header (\( -6 \)) by the column header (\( x \)). So, \( -6\times x = -6x \).

Step3: Verify the sum

Now, let's check if the sum of the middle row ( \( x^2 - 3x \)) and the bottom row ( \( -6x + 18 \)) gives the original quadratic \( x^2 - 9x + 18 \). Combining like terms: \( x^2+(-3x - 6x)+18 = x^2 - 9x + 18 \), which matches. So the missing terms are \( -3x \) and \( -6x \).

Answer:

C. \( -3x \) and \( -6x \)