Equations Involving Factored Expressions

Equations Involving Factored Expressions

Algebra I

Fill in the Blank

Solve for x. Write only the numeric answer in the space provided.

 $x-10=0$  

Fill in the Blank

Solve for x. Write only the numeric answer in the space provided.

 $\frac{x}{2}+20=0$  

What's the deal with this equation?

 $\left(x-10\right)\left(\frac{x}{2}+20\right)=0$  

• When multiplying two factors that result in a product of 0, at least one of the two factors must be 0.

• Zero-Product Property: If ab = 0, then a = 0, b = 0, or a and b = 0

• This extends to more factors as well.  

Example #1

Take time to analyze the example to the right.

Example #2

Take time to analyze the example to the right.

Multiple Select

 $x\left(x-3\right)=0$  

Identify the solution set to the equation. SELECT ALL THAT APPLY.

• -3

• 0

• 3

• 9

• 12

Multiple Select

 $x\left(x-3\right)\left(x+5\right)=0$  

Identify the solution set to the equation. SELECT ALL THAT APPLY.

• -5

• -3

• 0

• 3

• 5

Multiple Choice

 $\left(x+1\right)\left(x+2\right)=0$  

Pick the correct solution set.

• {-2, 1}

• {-2, -1, 0}

• {1, 2}

• {-2, -1}

• {-1, 2}

Multiple Choice

 $\left(x+4\right)\left(x-6\right)\left(x-10\right)=0$  

Pick the correct solution set.

• {-4, 6, 10}

• {-4, 0, 6, 10}

• {-10, -6, 4}

• {-4, -6, -10}

Multiple Select

 $x^2-6x=0$  

Select all possible solutions for x.
HINT: Consider factoring first

• 0

• -6

• 6

• 36

Multiple Select

 $15x^2+3x=0$  

Select all possible solutions for x.
HINT: Consider factoring first

• 0

•  $-\frac{1}{5}$  

• -3

• 5

Multiple Choice

Which equation has the following solution set:

{22, 53}

• $\left(x-22\right)\left(x-53\right)=0$

• $\left(x-22\right)\left(x+53\right)=0$

• $\left(x+22\right)\left(x+53\right)=0$

• $\left(x+22\right)\left(x-53\right)=0$
  

Multiple Choice

What is the best Thanksgiving food? Yes, there is one definitive answer.

• Turkey (Dry)

• Pie (Overrated)

• Mac & Cheese

• Cranberry Sauce (Ew)