High School Math : Intermediate Single-Variable Algebra

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #4 : Finding Roots

Find the zeros.

Possible Answers:

Correct answer:

Explanation:

Factor out a  from the entire equation. After that, you get . Factor the expression to . Set both of those equal to zero and your answers are  and

Example Question #5 : Finding Roots

Find the zeros.

Possible Answers:

Correct answer:

Explanation:

This expression is the difference of perfect squares. Therefore, it factors to. Set both of those equal to zero and your answers are  and .

Example Question #6 : Finding Roots

Find the zeros. 

Possible Answers:

Correct answer:

Explanation:

Factor the equation to . Set both equal to  and you get  and

Example Question #7 : Finding Roots

Find the zeros. 

Possible Answers:

Correct answer:

Explanation:

Factor a  out of the quation to get

 

which can be further factored to

.

Set the last two expressions equal to zero and you get  and

Example Question #8 : Finding Roots

Find the zeros. 

Possible Answers:

Correct answer:

Explanation:

Set each expression equal to zero and you get 0 and 6.

Example Question #9 : Finding Roots

Find the zeros.

Possible Answers:

Correct answer:

Explanation:

Set both expressions equal to . The first factor yields . The second factor gives you .

Example Question #10 : Finding Roots

Find the zeros. 

Possible Answers:

Correct answer:

Explanation:

Set both expressions to  and you get  and .

Example Question #11 : Solving Quadratic Equations

Solve the following equation by factoring.

Possible Answers:

Correct answer:

Explanation:

We can factor by determining the terms that will multiply to –8 and add to +7.

Our factors are +8 and –1.

Now we can set each factor equal to zero and solve for the root.

Example Question #12 : Solving Quadratic Equations

Solve the following equation by factoring.

Possible Answers:

Correct answer:

Explanation:

We know that one  term has a coefficient of 2 and that our factors must multiply to –10.

Our factors are +2 and –5.

Now we can set each factor equal to zero and solve for the root.

Example Question #13 : Solving Quadratic Equations

Solve the following equation by factoring.

Possible Answers:

Correct answer:

Explanation:

First, we can factor an term out of all of the values.

We can factor remaining polynomial by determining the terms that will multiply to +4 and add to +4.

Our factors are +2 and +2.

Now we can set each factor equal to zero and solve for the root.

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