College Algebra : Review and Other Topics

Study concepts, example questions & explanations for College Algebra

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Example Questions

Example Question #23 : Radicals

Add the radicals:

Possible Answers:

Correct answer:

Explanation:

In order to add or subtract, first simplify each radical completely. If the remaining number under the square root sign is the same for both numbers they can be added- much like with variables.

For this problem, it goes as follows:

Because both of these radicals are perfect squares, this becomes a simple problem.

Example Question #24 : Radicals

Add the radicals:

Possible Answers:

Correct answer:

Explanation:

In order to add or subtract, first simplify each radical completely. If the remaining number under the square root sign is the same for both numbers they can be added- much like with variables.

For this problem, it goes as follows:

Because both of these radicals are perfect squares, this becomes a simple problem.

Example Question #21 : Radicals

Add the radicals:

Possible Answers:

Correct answer:

Explanation:

In order to add or subtract, first simplify each radical completely. If the remaining number under the square root sign is the same for both numbers they can be added- much like with variables.

For this problem, it goes as follows:

In order to add, first simplify each radical as follows:

Since the radicals are the same, treat them like variables and add the "coefficients" in from of them to solve.

Example Question #26 : Radicals

Add the radicals:

Possible Answers:

Correct answer:

Explanation:

In order to add or subtract, first simplify each radical completely. If the remaining number under the square root sign is the same for both numbers they can be added- much like with variables.

For this problem, it goes as follows:

In order to add, first simplify the first radical as follows:

Since the radicals are the same, treat them like variables and add the "coefficients" in from of them to solve.

Example Question #21 : Radicals

Add the radicals:

Possible Answers:

Correct answer:

Explanation:

In order to add or subtract, first simplify each radical completely. If the remaining number under the square root sign is the same for both numbers they can be added- much like with variables.

For this problem, it goes as follows:

In order to add, first simplify the second radical as follows:

Since the radicals are the same, treat them like variables and add the "coefficients" in from of them to solve.

Example Question #21 : Radicals

Add: 

Possible Answers:

Correct answer:

Explanation:

Step 1: Break down all numbers inside the radicals into perfect squares and other numbers:

Step 2: Re-write the double of numbers outside, and the single repeated numbers inside the square root.

Step 3: Write the radicals in terms of the original function:

Step 4: Combine like terms:

Example Question #29 : Radicals

Add: 

Possible Answers:

None of the Above

Correct answer:

Explanation:

The first two terms are already in simplified form because the number in the radical cannot be broken down into numbers that have pairs.

We will only need to break down the last term...

 

We then replace  in the original equation with what we just calculated:

Add common terms, and then we have our final answer...

Example Question #71 : Review And Other Topics

Multiply the following polynomials:

Possible Answers:

Correct answer:

Explanation:

Multiply the following polynomials:

When multiplying polynomials, we need to multiply each term in the first polynomial by each term in the second polynomial. 

We can rewrite the expression as:

Next, actually do the multiplication.

Finally, combine like terms to get the following:

Example Question #1 : Polynomials

Identify the power of the following polynomial

Possible Answers:

Correct answer:

Explanation:

To find the power of a polynomial, you must find the term with the highest degree. Don't be fooled, you must distribute the power on the outside to the inside in order to find this term. Now, before you start worrying about foiling this 4 times, you can simply use the trick of distributing the outside power to the term on the inside with the largest power. Thus, our answer is:

Example Question #73 : Review And Other Topics

Multiply:

Possible Answers:

Correct answer:

Explanation:

This product can be rewritten as the sum of two expressions multiplied by their difference:

Apply the difference of squares pattern:

Apply the perfect square trinomial pattern on the left, and the Power of a Product Property on the right:

Collect like terms:

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