How to find the value of the coefficient - ACT Math
Card 0 of 9
What is the value of the coefficient in front of the term that includes 
in the expansion of 
?
What is the value of the coefficient in front of the term that includes
Using the binomial theorem, the term containing the _x_2 _y_7 will be equal to
(2_x_)2(–y)7
=36(–4_x_2 _y_7)= -144_x_2_y_7
Using the binomial theorem, the term containing the _x_2 _y_7 will be equal to
(2_x_)2(–y)7
=36(–4_x_2 _y_7)= -144_x_2_y_7
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Give the coefficient of 
in the binomial expansion of 
.
Give the coefficient of
If the expression 
is expanded, then by the binomial theorem, the 
term is
or, equivalently, the coefficient of 
is
Therefore, the 
coefficient can be determined by setting
If the expression
or, equivalently, the coefficient of
Therefore, the
Compare your answer with the correct one above
Give the coefficient of 
in the binomial expansion of 
.
Give the coefficient of
If the expression 
is expanded, then by the binomial theorem, the 
term is
or, equivalently, the coefficient of 
is
Therefore, the 
coefficient can be determined by setting
:
If the expression
or, equivalently, the coefficient of
Therefore, the
Compare your answer with the correct one above
Give the coefficient of 
in the product
.
Give the coefficient of
While this problem can be answered by multiplying the three binomials, it is not necessary. There are three ways to multiply one term from each binomial such that two 
terms and one constant are multiplied; find the three products and add them, as follows:
Add: 
.
The correct response is 
.
While this problem can be answered by multiplying the three binomials, it is not necessary. There are three ways to multiply one term from each binomial such that two
Add:
The correct response is
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Give the coefficient of 
in the product
.
Give the coefficient of
While this problem can be answered by multiplying the three binomials, it is not necessary. There are three ways to multiply one term from each binomial such that two 
terms and one constant are multiplied; find the three products and add them, as follows:
Add: 
The correct response is -122.
While this problem can be answered by multiplying the three binomials, it is not necessary. There are three ways to multiply one term from each binomial such that two
Add:
The correct response is -122.
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Give the coefficient of 
in the product
Give the coefficient of
While this problem can be answered by multiplying the three binomials, it is not necessary. There are three ways to multiply one term from each binomial such that two 
terms and one constant are multiplied; find the three products and add them, as follows:
Add: 
The correct response is 
.
While this problem can be answered by multiplying the three binomials, it is not necessary. There are three ways to multiply one term from each binomial such that two
Add:
The correct response is
Compare your answer with the correct one above
Give the coefficient of 
in the binomial expansion of 
.
Give the coefficient of
If the expression 
is expanded, then by the binomial theorem, the 
term is
or, equivalently, the coefficient of 
is
Therefore, the 
coefficient can be determined by setting
:
If the expression
or, equivalently, the coefficient of
Therefore, the
Compare your answer with the correct one above
A function of the form 
passes through the points 
and 
. What is the value of 
?
A function of the form
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
.
The easisest way to solve for
Using our first point, we will plug in
Squaring 0 gives us 0, and multiplying this by
We now know the value of
which simplifies to
However, since we know
subtracting 7 from both sides gives
and dividing by 4 gives our answer
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is equivalent to which of the following?
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 
.
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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