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Section 9.2 Worksheets

PDF Version of these Worksheets

Worksheet Worksheet 1
A4US

1.

Translate the diagram of algebra tiles into an equation.

2.

Use a diagram of algebra tiles to factor \(x^2 + 8x + 15\text{.}\) Draw the diagram and write the final equation.

3.

Fill in the appropriate value into the boxes, then use the method to factor the given quadratic polynomial using a complete presentation.

\begin{equation*} x^2 + 8x + 15 \longrightarrow \left\{ \begin{array}{l} \text{Multiply to $\boxed{\strut \phantom{.....}}$} \\ \text{Add to $\boxed{\strut \phantom{.....}}$} \end{array} \right. \end{equation*}

Worksheet Worksheet 2
A4US

1.

Use a diagram of algebra tiles to factor \(2x^2 + 9x + 4\text{.}\) Draw the diagram and write the final equation.

2.

Fill in the appropriate value into the boxes, then use the method to factor the given quadratic polynomial using a complete presentation.

\begin{equation*} x^2 + 2x - 8 \longrightarrow \left\{ \begin{array}{l} \text{Multiply to $\boxed{\strut \phantom{.....}}$} \\ \text{Add to $\boxed{\strut \phantom{.....}}$} \end{array} \right. \end{equation*}

3.

Fill in the appropriate value into the boxes, then use the method to factor the given quadratic polynomial using a complete presentation.

\begin{equation*} 2x^2 - 3x - 27 \longrightarrow \left\{ \begin{array}{l} \text{Multiply to $\boxed{\strut \phantom{.....}}$} \\ \text{Add to $\boxed{\strut \phantom{.....}}$} \end{array} \right. \end{equation*}

Worksheet Worksheet 3
A4US

1.

Fill in the appropriate value into the boxes, then use the method to factor the given quadratic polynomial using a complete presentation.

\begin{equation*} x^2 - 8x + 7 \longrightarrow \left\{ \begin{array}{l} \text{Multiply to $\boxed{\strut \phantom{.....}}$} \\ \text{Add to $\boxed{\strut \phantom{.....}}$} \end{array} \right. \end{equation*}

2.

Fill in the appropriate value into the boxes, then use the method to factor the given quadratic polynomial using a complete presentation.

\begin{equation*} 2x^2 + 5x + 2 \longrightarrow \left\{ \begin{array}{l} \text{Multiply to $\boxed{\strut \phantom{.....}}$} \\ \text{Add to $\boxed{\strut \phantom{.....}}$} \end{array} \right. \end{equation*}

3.

Use the method to factor \(x^2 - 7x + 10\) using a complete presentation.

Worksheet Worksheet 4
A4US

1.

Fill in the appropriate value into the boxes, then use the method to factor the given quadratic polynomial using a complete presentation.

\begin{equation*} 3x^2 - 10x - 8 \longrightarrow \left\{ \begin{array}{l} \text{Multiply to $\boxed{\strut \phantom{.....}}$} \\ \text{Add to $\boxed{\strut \phantom{.....}}$} \end{array} \right. \end{equation*}

2.

Use the \(ac\) method to factor \(x^2 + 6x + 9\) using a complete presentation.

3.

Use the \(ac\) method to factor \(x^2 - 3x - 40\) using a complete presentation.

4.

Use the \(ac\) method to factor \(2x^2 - 5x - 3\) using a complete presentation.

Worksheet Worksheet 5
A4US

1.

Use the \(ac\) method to factor \(x^2 + 9x + 20\) using a complete presentation.

2.

Use the \(ac\) method to factor \(4x^2 - 4x - 3\) using a complete presentation.

3.

Factor \(x^2 + 10x + 16\) and \(x^2 - 10x + 16\text{,}\) then compare the results. What do you notice about the factorizations?

4.

Factor \(x^2 - 5x - 14\) and \(x^2 + 5x - 14\text{,}\) then compare the results. What do you notice about the factorizations?

Worksheet Worksheet 6
A4US

1.

Suppose you are trying to factor a quadratic that has the following condition:

\begin{equation*} \left\{ \begin{array}{l} \text{Multiply to a positive number} \\ \text{Add to a positive number} \end{array} \right. \end{equation*}

What information can you conclude about the signs of the two numbers you're looking for?

2.

Suppose you are trying to factor a quadratic that has the following condition:

\begin{equation*} \left\{ \begin{array}{l} \text{Multiply to a positive number} \\ \text{Add to a negative number} \end{array} \right. \end{equation*}

What information can you conclude about the signs of the two numbers you're looking for?

3.

Suppose you are trying to factor a quadratic that has the following condition:

\begin{equation*} \left\{ \begin{array}{l} \text{Multiply to a negative number} \\ \text{Add to a positive number} \end{array} \right. \end{equation*}

What information can you conclude about the signs of the two numbers you're looking for?

4.

Suppose you are trying to factor a quadratic that has the following condition:

\begin{equation*} \left\{ \begin{array}{l} \text{Multiply to a negative number} \\ \text{Add to a negative number} \end{array} \right. \end{equation*}

What information can you conclude about the signs of the two numbers you're looking for?