Question

question 3 of 5

type the correct answer in each box. use numerals instead of words.

what is the product of \\((x - 5)\\) and \\((x - 4)\\)? use the model to find the result.

Explanation:

⚡ Using what you learned: multiplying polynomials

Step 1: Fill in the area model boxes

Multiply the row headers by the column headers to find the value for each box:

• Top-right box:

$$ x \cdot (-4) = -4x $$

• Bottom-left box:

$$ -5 \cdot x = -5x $$

• Bottom-right box:

$$ -5 \cdot (-4) = 20 $$

Step 2: Combine like terms

Sum the terms inside the model to find the total product:

$$ x^2 + (-4x) + (-5x) + 20 $$

Combine the \( x \)-terms:

$$ -4x - 5x = -9x $$

The simplified expression is:

$$ x^2 - 9x + 20 $$

To match the format \( x^2 + \square x + \square \):

$$ x^2 + (-9)x + 20 $$

Answer:

• Top-right box: -4x
• Bottom-left box: -5x
• Bottom-right box: 20
• Bottom equation boxes: \( x^2 + \) -9 \( x + \) 20