High School Math : Intermediate Single-Variable Algebra

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #10 : Simplifying Polynomials

Simplify the following polynomial:

Possible Answers:

Correct answer:

Explanation:

To simplify the polynomial, begin by rearranging the terms to have positive exponents:

 

Now, combine like terms:

 

Simplify the integers:

Example Question #11 : Simplifying Polynomials

Simplify the following polynomial: 

Possible Answers:

Correct answer:

Explanation:

Begin by reversing the numerator and denominator so that the exponents are positive:

Square the right side of the expression and multiply:

Simplify:

Example Question #12 : Simplifying Polynomials

Simplify the following polynomial: 

Possible Answers:

Correct answer:

Explanation:

Begin by simplifying the integers:

Subtract the exponent in the denominator from the exponent in the numerator:

Example Question #13 : Simplifying Polynomials

Simplify the following polynomial: 

Possible Answers:

Correct answer:

Explanation:

Begin by multiplying the terms:

Convert into fraction form:

Example Question #14 : Simplifying Polynomials

Simplify the following polynomial:

Possible Answers:

Correct answer:

Explanation:

Use the FOIL method to multiply the terms: F (first) O (outer) I (inner) L (last)

Example Question #15 : Simplifying Polynomials

Simplify the following polynomial: 

Possible Answers:

Correct answer:

Explanation:

Use the FOIL method to multiply the terms: F (first) O (outer) I (inner) L (last)

Combine like terms:

Example Question #16 : Simplifying Polynomials

If and , what is ?

Possible Answers:

Correct answer:

Explanation:

is a composite function solved by substituting into :

Example Question #1 : Factoring Polynomials

Factor

Possible Answers:

Cannot be Factored

Correct answer:

Explanation:

Use the difference of perfect cubes equation:

In ,

 and

Example Question #2 : Factoring Polynomials

Factor the polynomial completely and solve for .

Possible Answers:

Correct answer:

Explanation:

To factor and solve for  in the equation 

Factor  out of the equation

Use the "difference of squares" technique to factor the parenthetical term, which provides the completely factored equation:

Any value that causes any one of the three terms , and  to be  will be a solution to the equation, therefore

Example Question #3 : Factoring Polynomials

Factor the following expression:

Possible Answers:

Correct answer:

Explanation:

You can see that each term in the equation has an "x", therefore by factoring "x" from each term you can get that the equation equals .

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