Question

drag the tiles to the correct boxes. not all tiles will be used.

determine which steps are used to find the product shown. put the steps in the order in which they would be performed.

\\\frac{x^2 + 7x + 10}{x^2 + 4x + 4} \cdot \frac{x^2 + 3x + 2}{x^2 + 6x + 5}\\

tiles:
\\\frac{(x + 2)(x + 5)}{(x + 2)(x + 2)} \cdot \frac{(x + 1)(x + 2)}{(x + 5)(x + 1)}\\
\\\frac{(x + 5)(x + 2)}{(x + 2)(x + 5)}\\
\\\frac{(x + 5)(x + 2)}{(x + 5)}\\
\\x + 2\\
\\\frac{(x + 7)(x + 1)}{(x + 4)(x + 2)}\\
\\1\\
\\\frac{(x + 7)(x + 1)}{(x + 4)(x + 1)} \cdot \frac{(x + 3)(x + 1)}{(x + 3)(x + 2)}\\
\\\frac{(x + 5)}{(x + 2)} \cdot \frac{(x + 2)}{(x + 5)}\\

Explanation:

Factor all quadratic polynomials

$$
LATEXBLOCK0
$$

Multiply and simplify the factored expression

$$
LATEXBLOCK1
$$

Answer:

Determine which steps are used to find the product shown. Put the steps in the order in which they would be performed.

$$\frac{x^2+7x+10}{x^2+4x+4} \cdot \frac{x^2+3x+2}{x^2+6x+5}$$

• Step 1: \(\frac{(x+2)(x+5)}{(x+2)(x+2)} \cdot \frac{(x+1)(x+2)}{(x+5)(x+1)}\)
• Step 2: \(\frac{(x+5)(x+2)}{(x+2)(x+5)}\)
• Step 3: <blank>\(\frac{(x+5)}{(x+2)} \cdot \frac{(x+2)}{(x+5)}\)</blank>
• Step 4: <blank>\(1\)</blank>