Algebra II : Intermediate Single-Variable Algebra
Study concepts, example questions & explanations for Algebra II
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Example Questions
Example Question #31 : Simplifying Polynomials
Simplify the polynomial. Assume that no variable equals zero.
It is important to remember that ;
Example Question #32 : Simplifying Polynomials
Simplify:
To simplify this expression, first identify what all the terms have in common. In this case, it's 2x. Now, factor that out from each of the terms to get your answer: 
Example Question #33 : Simplifying Polynomials
Simplify:
To simplify, first use the distributive property: 
Example Question #34 : Simplifying Polynomials
Put the following polynomial into standard form:
Example Question #35 : Simplifying Polynomials
Write the polynomial in standard form that has zeroes at 3, and 
From the zeroes we know:
First use FOIL method to simplify terms containing irrational numbers:
Which simplifies to:
FOIL again:
Example Question #36 : Simplifying Polynomials
Simplify 
We can start by factoring a 
Then we can factor the quadratic that's left in the denominator and cancel the one of the terms with the term in the numerator:
Example Question #37 : Simplifying Polynomials
If 
We should start by writing everything out so we can have a good look at it:
To factor the numerator, let's group the first two and the last two terms:
We can factor out a 
Now we can factor out the 
We can then cancel the 
Example Question #38 : Simplifying Polynomials
Simplify the polynomial:
To simplify the polynomial expression, we can simplify each term individually. To start, the first term has a difference of squares in the numerator, which can be rewritten as
using the formula
We can now simplify the first term completely to 
The second term can now be simplified:
Note that one could also simplify the denominator by itself by finding the least common denominator, and then simplify the entire term.
Now that all the terms are simplified, our final answer is
Example Question #34 : Simplifying Polynomials
Simplify:
To simplify this expression, identify what goes into every one of the terms.
In this case, it's -7.
Then, take that out from each of the terms, remembering to pay attention to the signs.
Therefore, your answer is:
Example Question #35 : Simplifying Polynomials
Simplify:
First, distribute the -1 at the front of the second expression:
Then, combine like terms to get your answer of
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