High School Math : Intermediate Single-Variable Algebra

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #31 : Intermediate Single Variable Algebra

Factor the following polynomial:

Possible Answers:

Correct answer:

Explanation:

Begin by rearranging the terms to group together the quadratic:

 

Now, convert the quadratic into a square:

 

Finally, distribute the :

Example Question #32 : 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 #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 #1 : Write A Polynomial Function From Its Zeros

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 #2 : 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 #3 : Quadratic Equations And Inequalities

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 #4 : Quadratic Equations And Inequalities

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 #5 : Quadratic Equations And Inequalities

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 #6 : Quadratic Equations And Inequalities

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.

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