ACT Math : Polynomial Operations
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Example Questions
Example Question #1 : How To Subtract Polynomials
Simplify:
Begin by distributing the subtraction of the second term in this question:
Now, you merely need to combine like terms:
Example Question #2 : How To Subtract Polynomials
If 
To solve this equation, we substitute 
Therefore the new equation would read
Now we must square the expression 
We must now plug in our new value for 
Now we must distribute the 
Therefore, our answer is 
Example Question #3 : How To Subtract Polynomials
The expression 
To answer this question, we must distribute the 
To distribute a variable or number, you multiply that value with every other value within the brackets or parentheses. So, for this data:
We then simplify the expression by combining the variables we are multiplying together into expressions. For this data:
Be sure to keep all of your operations the same within the problem itself, unless the number being distributed is negative, which will then switch the signs with the brackets from positive to negative or negative to positive.
Therefore, our answer is 
Example Question #4 : How To Subtract Polynomials
Solve the equation
To answer this question, we are solving for the values of 
To this, we need to get 
Now we can divide both sides by 
Therefore, the answer to this question is
Example Question #1 : How To Add Polynomials
Simplify the following expression.
Line up each expression vertically. Then combine like terms to solve.
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Thus, the final solution is 
Example Question #2 : How To Add Polynomials
What is the value of 
In adding 
. . .and adding 
. . .the variables are isolated to become:
After dividing both sides by 
Example Question #3 : How To Add Polynomials
Add the following polynomials:
This is a problem where elimination can be help you save a little time. You can eliminate options quickly by simplifying one power at a time and comparing your work with the answer choices.
To begin, reorder the problem so that all like terms are next to each other. When doing so, keep an eye on your signs so that you don't accidentally make a mistake.
From here, combine each pair of terms. As you do so, compare your work with the answer choices.
Once you put all of your solutions together, the correct answer looks like this:
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