High School Math : Intermediate Single-Variable Algebra

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #7 : Quadratic Equations And Inequalities

FOIL .

Possible Answers:

Correct answer:

Explanation:

Remember FOIL stands for First Outer Inner Last. That means we can take  and turn it into .

Simplify to get .

Example Question #8 : Quadratic Equations And Inequalities

FOIL .

Possible Answers:

Correct answer:

Explanation:

 is the same thing as .

Remember that FOIL stands for First Outer Inner Last.

For this problem, that would be 

Simplify that to .

Example Question #9 : Quadratic Equations And Inequalities

FOIL .

Possible Answers:

Correct answer:

Explanation:

Remember that FOIL stands for First Outer Inner Last.

For this problem that would give us:

Simplify.

Example Question #10 : Quadratic Equations And Inequalities

FOIL .

Possible Answers:

Correct answer:

Explanation:

Remember that FOIL stands for First Outer Inner Last.

For this problem that would give us:

Simplify:

 

 

Example Question #1 : Simplifying And Expanding Quadratics

Solve the equation for .

Possible Answers:

Correct answer:

Explanation:

Cross multiply.

Set the equation equal to zero.

Factor to find the roots of the polynomial.

 and

Example Question #1 : Foil

Evaluate 

Possible Answers:

Correct answer:

Explanation:

In order to evaluate  one needs to multiply the expression by itself using the laws of FOIL.  In the foil method, one multiplies in the following order: first terms, outer terms, inner terms, and last terms.

Multiply terms by way of FOIL method.

Now multiply and simplify.

Example Question #41 : Intermediate Single Variable Algebra

Expand .

Possible Answers:

Correct answer:

Explanation:

To solve our given equation, we need to use FOIL (First, Outer, Inner, Last).

Combine like terms.

Example Question #42 : Intermediate Single Variable Algebra

FOIL .

Possible Answers:

Correct answer:

Explanation:

Remember FOIL stands for First Outer Inner Last.

Combine like terms to get .

Example Question #1 : Understanding The Discriminant

Use the discriminant to determine the nature of the roots:

Possible Answers:

 imaginary roots

 rational roots

 irrational roots

 rational root

 imaginary root

Correct answer:

 irrational roots

Explanation:

The formula for the discriminant is:

Since the discriminant is positive and not a perfect square, there are  irrational roots.

Example Question #2 : Understanding The Discriminant

Use the discriminant to determine the nature of the roots:

Possible Answers:

 irrational roots

 rational roots

 imaginary root

 rational root

 imaginary roots

Correct answer:

 imaginary roots

Explanation:

The formula for the discriminant is:

Since the discriminant is negative, there are  imaginary roots.

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