### All High School Math Resources

## Example Questions

### Example Question #10 : Simplifying Polynomials

Simplify the following polynomial:

**Possible Answers:**

**Correct answer:**

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:**

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:**

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:**

Begin by multiplying the terms:

Convert into fraction form:

### Example Question #14 : Simplifying Polynomials

Simplify the following polynomial:

**Possible Answers:**

**Correct answer:**

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:**

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:**

is a composite function solved by substituting into :

### Example Question #1 : Factoring Polynomials

Factor

**Possible Answers:**

Cannot be Factored

**Correct answer:**

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:**

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:**

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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