High School Math : Algebra II

Study concepts, example questions & explanations for High School Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #33 : Intermediate Single Variable Algebra

Factor the following polynomial:

Possible Answers:

Correct answer:

Explanation:

Begin by extracting  from the polynomial:

 

Now, rearrange to combine like terms:

 

Extract the like terms and factor the cubic:

 

Simplify by combining like terms:

Example Question #711 : Intermediate Single Variable Algebra

Consider the equation .

According to the Rational Zeroes Theorem, if  are all integers, then, regardless of their values, which of the following cannot be a solution to the equation?

Possible Answers:

Correct answer:

Explanation:

By the Rational Zeroes Theorem, any rational solution must be a factor of the constant, 6, divided by the factor of the leading coefficient, 14. 

Four of the answer choices have this characteristic:

is in lowest terms, and 3 is not a factor of 14. It is therefore the correct answer.

Example Question #1 : Quadratic Equations And Inequalities

Solve the following equation using the quadratic form:

Possible Answers:

Correct answer:

Explanation:

Factor the equation and solve:

 or

Therefore there are four answers:

Example Question #1 : Quadratic Equations And Inequalities

Solve the following equation using the quadratic form:

Possible Answers:

Correct answer:

Explanation:

Factor the equation and solve:

or

This has no solutions.

Therefore there is only one answer:

Example Question #1 : Using 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 #2 : Using 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.  Be sure to pay attention to signs.

Multiply terms by way of FOIL method.

Now multiply and simplify, paying attention to signs.

Example Question #2 : Using 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.  Be sure to pay attention to signs.

Multiply terms by way of FOIL method.

Now multiply and simplify, paying attention to signs.

Example Question #4 : Understanding Quadratic Equations

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.  Be sure to pay attention to signs.

Multiply terms by way of FOIL method.

Now multiply and simplify, paying attention to signs.

Example Question #281 : Algebra Ii

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 #42 : Intermediate Single Variable Algebra

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 .

Learning Tools by Varsity Tutors