ACT Math : Polynomials

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #2 : How To Subtract Polynomials

Simplify:

Possible Answers:

Correct answer:

Explanation:

Begin by distributing the subtraction of the second term in this question:

Now, you merely need to combine like terms:

Example Question #3 : How To Subtract Polynomials

If , then what does  equal?

Possible Answers:

Correct answer:

Explanation:

To solve this equation, we substitute  in for every instance of  seen in the original equation .

Therefore the new equation would read 

Now we must square the expression . To do this, you must multiply the expression by itself. Therefore:

We must now plug in our new value for  into our original equation in place of .

Now we must distribute the  into . To do this, you multiply each expression within the parenthesis by :

Therefore, our answer is .

Example Question #4 : How To Subtract Polynomials

The expression  is equivalent to which of the following?

Possible Answers:

Correct answer:

Explanation:

To answer this question, we must distribute the  to the rest of the variables , , and  that are within the brackets.

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 #5 : How To Subtract Polynomials

Solve the equation 

Possible Answers:

Correct answer:

Explanation:

To answer this question, we are solving for the values of  that make this equation true.

To this, we need to get  on a side by itself so we can evaluate it. To do this, we first add  to both sides so that we can then begin to deal with the  value. So, for this data:

can also be written as . Therefore:

Now we can divide both sides by  and find the value of .

Therefore, the answer to this question is 

Example Question #1 : How To Add Polynomials

Simplify the following expression. 

Possible Answers:

Correct answer:

Explanation:

Line up each expression vertically. Then combine like terms to solve. 

____________________

 

Thus, the final solution is .

Example Question #2 : How To Add Polynomials

What is the value of  when 

Possible Answers:

Correct answer:

Explanation:

In adding  to both sides:

. . .and adding  to both sides:

. . .the variables are isolated to become:

 

After dividing both sides by , the equation becomes:

Example Question #31 : Variables

Add the following polynomials:

Possible Answers:

Correct answer:

Explanation:

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.

   Eliminate any answer choices that have a different  term.

 Eliminate any answer choices that have a different  term.

 Eliminate any answer choices that have a different x term.

 Eliminate any answer choices that have a different constant term.

Once you put all of your solutions together, the correct answer looks like this:

Example Question #1 : Binomials

What is the value of the coefficient in front of the term that includes in the expansion of ?

 

Possible Answers:

Correct answer:

Explanation:

Using the binomial theorem, the term containing the x2 ywill be equal to

 Act_math_113_14(2x)2(–y)7

=36(–4x2 y7)= -144x2y7

Example Question #1 : How To Find The Value Of The Coefficient

A function of the form  passes through the points  and .  What is the value of  ?

Possible Answers:

Correct answer:

Explanation:

The easisest way to solve for  is to begin by plugging each pair of coordinates into the function.

Using our first point, we will plug in  for  and  for .  This gives us the equation

.

Squaring 0 gives us 0, and multiplying this by  still gives 0, leaving only  on the right side, such that

.

We now know the value of , and we can use this to help us find .  Substituting our second set of coordinates into the function, we get

 which simplifies to

.

However, since we know , we can substitute to get

subtracting 7 from both sides gives

and dividing by 4 gives our answer

.

Example Question #2 : Binomials

 is equivalent to which of the following?

Possible Answers:

Correct answer:

Explanation:

To answer this problem, we need to multiply the expressions together, being mindful of how to correctly multiply like variables with exponents. To do this, we add the exponents together if the the like variables are being multiplied and subtract the exponents if the variables are being divided. So, for the presented data:

We then multiply the remaining expressions together. When we do this, we will multiply the coefficients together and combine the different variables into the final expression. Therefore:

This means our answer is .

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