Algebra II : Polynomials

Example Questions

Example Question #41 : Simplifying Polynomials

Simplify:

Possible Answers:

Correct answer:

Explanation:

To simplify, first remember to distribute the negative sign in front of the second set of terms:

.

Then, combine like terms.

Your answer is:

.

Example Question #42 : Simplifying Polynomials

Simplify:

Possible Answers:

Correct answer:

Explanation:

To simplify this expression, first identify the greatest common factor for this set of terms.

In this case, it's 4.

Then, factor 4 out of each of the terms to get your answer of:

.

Example Question #41 : Simplifying Polynomials

Simplify:

Possible Answers:

Correct answer:

Explanation:

In order to multiply both terms, first distribute the first term of the first polynomial with the the second polynomial.

Repeat the process for the second and third terms.

Add all the trinomials together and combine like-terms.

The answer is:

Example Question #1181 : Algebra Ii

Simplify:

Possible Answers:

Correct answer:

Explanation:

To simplify this expression, combine all like terms:

Put your simplified terms together:

Example Question #41 : Simplifying Polynomials

Simplify:

Possible Answers:

Correct answer:

Explanation:

The first step here is to use the distributive property:

Now combine your like terms to get your final answer:

Example Question #42 : Simplifying Polynomials

Simplify the polynomial.

Possible Answers:

Correct answer:

Explanation:

Simplify the polynomial.

Step 1: Rearrange the expression so that like terms are next to each other.

Remember: Like terms are terms with the same type of variable.

Step 2: Simplify by adding or subtracting like terms.

Solution:

Example Question #47 : Simplifying Polynomials

Simplify this polynomial:

Possible Answers:

None of the other answers.

Correct answer:

Explanation:

In order to correctly simplify this problem you must pay attention to which terms are actually considered "like terms" and pay attention to signs. For instance 6x and 6x^2 are not like terms. Neither are 3 and 3x.

Start by distributing within the parenthesis:

Next simplify the like terms based on your preference. We will start with the highest powers (largest exponents):

Now the squared exponents:

Now the x terms cancel and simplify the constants:

Example Question #1 : Factoring Polynomials

Find the zeros.

Possible Answers:

Correct answer:

Explanation:

This is a difference of perfect cubes so it factors to . Only the first expression will yield an answer when set equal to 0, which is 1. The second expression will never cross the -axis. Therefore, your answer is only 1.

Example Question #2 : Factoring Polynomials

Find the zeros.

Possible Answers:

Correct answer:

Explanation:

Factor the equation to . Set  and get one of your 's to be . Then factor the second expression to . Set them equal to zero and you get

Example Question #1 : Factoring Polynomials

Factor the polynomial:

Possible Answers:

Correct answer:

Explanation:

First, begin by factoring out a common term, in this case :

Then, factor the terms in parentheses by finding two integers that sum to and multiply to :