Polynomials - ACT Math
Card 0 of 756
Solve for x when 6x – 4 = 2x + 5
Solve for x when 6x – 4 = 2x + 5
Solve by simplifying:
6x – 4 = 2x + 5
6x = 2x + 9
4x = 9
x = 9/4
Solve by simplifying:
6x – 4 = 2x + 5
6x = 2x + 9
4x = 9
x = 9/4
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What is the value of the following equation if 
and 
?
What is the value of the following equation if
Substitute the numbers 3 and –4 for t and v, respectively.
Substitute the numbers 3 and –4 for t and v, respectively.
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Simplify the following binomial:
Simplify the following binomial:
The equation that is presented is:
To get the correct answer, you first need to combine all of the like terms. So, you can subtract the 
from the 
, leaving you with:
From there, you can reduce the numbers by their greatest common denominator, in this case, 
:
Then you have arrived at your final answer.
The equation that is presented is:
To get the correct answer, you first need to combine all of the like terms. So, you can subtract the
From there, you can reduce the numbers by their greatest common denominator, in this case,
Then you have arrived at your final answer.
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Simplify the following binomial:
Simplify the following binomial:
The equation presented in the problem is:
First you have to combine the like terms, i.e. combining all instances of 
and 
:
Then, you can factor out the common 
to get your answer
The equation presented in the problem is:
First you have to combine the like terms, i.e. combining all instances of
Then, you can factor out the common 
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Simplify the following binomial expression:
Simplify the following binomial expression:
First, combine all of the like terms that you are able:
Then, reduce by the greatest common denominator (in this case, 
):
First, combine all of the like terms that you are able:
Then, reduce by the greatest common denominator (in this case,
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A hockey team has 12 forwards, 6 defensemen, and 2 goalies. When they place 3 forwards, 2 defensemen, and 1 goalie on the ice, how many of each type are on the bench, (not on the ice)? F=Forward, D = Defensemen, G= Goalie
A hockey team has 12 forwards, 6 defensemen, and 2 goalies. When they place 3 forwards, 2 defensemen, and 1 goalie on the ice, how many of each type are on the bench, (not on the ice)? F=Forward, D = Defensemen, G= Goalie
We can represent this as a subtraction of trinomials.
(12F + 6D + 2G) – (3F + 2D + 1G) = 9F + 4D + 1G.
We can represent this as a subtraction of trinomials.
(12F + 6D + 2G) – (3F + 2D + 1G) = 9F + 4D + 1G.
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You go to the grocery store and pick up 
apples, 
peaches, and 
oranges. Today you had some friends over who ate 
apples, 
peaches, and 
oranges. Which of the following represents how many of each you now have left if 
= apples, 
= peaches, and 
= oranges?
You go to the grocery store and pick up
1. Represent the situation with two sets of trinomials:
Before your friends ate the fruit:
The fruit your friends ate:
2. Subtract the first trinomial from the second trinomial:
1. Represent the situation with two sets of trinomials:
Before your friends ate the fruit:
The fruit your friends ate:
2. Subtract the first trinomial from the second trinomial:
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Choose the answer which best simplifies the following expression:
Choose the answer which best simplifies the following expression:
To solve this expression, merely remove the parentheses (bearing in mind that because the second trinomial is being subtracted, it will be negative) and combine like terms:
To solve this expression, merely remove the parentheses (bearing in mind that because the second trinomial is being subtracted, it will be negative) and combine like terms:
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Choose the answer which best simplifies the following expression:
Choose the answer which best simplifies the following expression:
To simplify, remove parentheses and combine like terms:
To simplify, remove parentheses and combine like terms:
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Choose the answer which best simplifies the following expression:
Choose the answer which best simplifies the following expression:
To simplify, remove parentheses and combine like terms:
To simplify, remove parentheses and combine like terms:
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Simplify the following:
Simplify the following:
To multiply trinomials, simply foil out your factored terms by multiplying each term in one trinomial to each term in the other trinomial. I will show this below by spliting up the first trinomial into its 3 separate terms and multiplying each by the second trinomial.
Now we treat this as the addition of three monomials multiplied by a trinomial.
Now combine like terms and order by degree, largest to smallest.
To multiply trinomials, simply foil out your factored terms by multiplying each term in one trinomial to each term in the other trinomial. I will show this below by spliting up the first trinomial into its 3 separate terms and multiplying each by the second trinomial.
Now we treat this as the addition of three monomials multiplied by a trinomial.
Now combine like terms and order by degree, largest to smallest.
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Solve: 
Solve:
The 
is distributed and multiplied to each term 
, 
, and 
.
The
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Which of the following is equal to 
?
Which of the following is equal to
is multiplied to both 
and 
and 
is only multiplied to 
.
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What is 
?
What is
is distributed first to 
and 
is distributed to 
. This results in 
and 
. Like terms can then be added together. When added together, 
, 
, and 
. This makes the correct answer 
.
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Find the degree of the polynomial:
Find the degree of the polynomial:
The degree of a polynomial is determined by the term with the highest degree. In this case that is 
, which has a degree of 
.
The degree of a polynomial is determined by the term with the highest degree. In this case that is
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What type of equation is the following?
(y + 2)(y + 4)(y + 1) = z
What type of equation is the following?
(y + 2)(y + 4)(y + 1) = z
The degree of a polynomial is the highest exponent of the terms.
Degree 0 – constant
Degree 1 – linear
Degree 2 – quadratic
Degree 3 – cubic
Degree 4 – quartic
Multiply out the equation:
(y + 2)(y + 4)(y + 1) = z
(y2 + 2y + 4y + 8)(y + 1) = z
y3 + 2y2 + 4y2 + 8y + y2 + 2y + 4y + 8 = z
The highest exponent is y3;therefore the equation is a degree 3 cubic.
The degree of a polynomial is the highest exponent of the terms.
Degree 0 – constant
Degree 1 – linear
Degree 2 – quadratic
Degree 3 – cubic
Degree 4 – quartic
Multiply out the equation:
(y + 2)(y + 4)(y + 1) = z
(y2 + 2y + 4y + 8)(y + 1) = z
y3 + 2y2 + 4y2 + 8y + y2 + 2y + 4y + 8 = z
The highest exponent is y3;therefore the equation is a degree 3 cubic.
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What is the degree of the following polynomial?
What is the degree of the following polynomial?
The degree of a polynomial is determined by the term with the highest degree. In this case, the first term, 
, has the highest degree, 
. The degree of a term is calculated by adding the exponents of each variable in the term.
The degree of a polynomial is determined by the term with the highest degree. In this case, the first term,
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Simplify:
Simplify:
When subtracting polynomials, it's helpful to remember that the "minus sign" gets distributed. It's as if the two polynomials are being added and a -1 is in front of the second polynomial.
This -1 will get multiplied to all the terms in the second polynomial that is being subtracted from the first, so it becomes 
. You may note that by multiplying by -1, every term in the polynomial switches its original sign. The problem then becomes:
From here, in order to simplify, because there's no equal sign, it can be deduced that we are not working toward a solution for x. The original problem is presented as an expression so an expression as an answer will be expected. In order to work towards a final simplified expression, like terms must be collected. This will provide the final answer.
When subtracting polynomials, it's helpful to remember that the "minus sign" gets distributed. It's as if the two polynomials are being added and a -1 is in front of the second polynomial.
This -1 will get multiplied to all the terms in the second polynomial that is being subtracted from the first, so it becomes
From here, in order to simplify, because there's no equal sign, it can be deduced that we are not working toward a solution for x. The original problem is presented as an expression so an expression as an answer will be expected. In order to work towards a final simplified expression, like terms must be collected. This will provide the final answer.
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Simplify:
Simplify:
Begin by distributing the subtraction of the second term in this question:
Now, you merely need to combine like terms:
Begin by distributing the subtraction of the second term in this question:
Now, you merely need to combine like terms:
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The expression 
is equivalent to which of the following?
The expression
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 
.
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
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