The coefficient of a term is the number part of a term, including its sign. For instance, the coefficient of is , and the coefficient of is
Every term has a coefficient, even if it has no numerical part. For example:
The coefficient of is because is equivalent to
The coefficient of is because is equivalent to
List the coefficients of the expression
The terms of the expression are and Looking at each term individually, we see that
the coefficient of the term is , and
the coefficient of the term is
So, the coefficients of the expression are and
What is the coefficient of $t$ in the expression $4r+3t-2s?$
|
a
|
$5$ |
|
b
|
$3t$ |
|
c
|
$-2$ |
|
d
|
$4$ |
|
e
|
$3$ |
The coefficient of $j$ in the expression $-j + 5k + 10l - 1$ is
|
a
|
$-2$ |
|
b
|
$1$ |
|
c
|
$-j$ |
|
d
|
$-1$ |
|
e
|
$j$ |
The coefficients of the expression $4a + 7b$ are
|
a
|
$4$ and $a$ |
|
b
|
$a$ and $b$ |
|
c
|
$4a$ and $7b$ |
|
d
|
$4$ and $7$ |
|
e
|
$7$ and $b$ |
What are the coefficients of and in the expression
The terms of the expression are and Looking at each term individually, we see that
the coefficient of the term is ,
the coefficient of the term is and
the coefficient of the term is
So, the coefficients of and in the given expression are and respectively.
What is the coefficient of $y$ in the expression $\dfrac{x}{2}-\dfrac{3y}{4}+\dfrac{11z}{8}?$
|
a
|
$-\dfrac{3}{4}$ |
|
b
|
$\dfrac{11}{8}$ |
|
c
|
$\dfrac{3}{4}$ |
|
d
|
$\dfrac{y}{2}$ |
|
e
|
$\dfrac{3y}{4}$ |
The coefficients of $z$ and $w$ in the expression $z +\dfrac{w}2$ are
|
a
|
|
|
b
|
|
|
c
|
|
|
d
|
|
|
e
|
What is the sum of the coefficients in the expression $\dfrac{p}{4}-\dfrac{3q}{8}?$
|
a
|
$\dfrac14$ |
|
b
|
$\dfrac{p-q}4$ |
|
c
|
$-\dfrac{3}{8}$ |
|
d
|
$p+q$ |
|
e
|
$-\dfrac18$ |
The constant terms of a linear expression are terms that contain no variables.
For example, in the expression
the constant terms are and
What is the value of the constant term in the expression
The expression has four terms: , , and The only term that does not contain any variables is , so is the constant term.
What is the constant term in the expression $6p -8 +3q?$
|
a
|
$3q$ |
|
b
|
$6$ |
|
c
|
$8p$ |
|
d
|
$-8$ |
|
e
|
$3$ |
What is the constant term in the expression $11r-3s+7t+1?$
|
a
|
$11$ |
|
b
|
$7t$ |
|
c
|
$-3r$ |
|
d
|
$1$ |
|
e
|
$11r$ |
What is the constant term in the expression $a-2+3b-4c?$
|
a
|
$-2$ |
|
b
|
$3b$ |
|
c
|
$3$ |
|
d
|
$2$ |
|
e
|
$-4$ |
If a variable is missing from an expression, then its coefficient is zero. For example, in the expression the coefficient of is because does not appear in the expression.
To understand why the coefficient of a missing variable is always zero, remember the following:
Zero times any number (or variable) is zero. So is equal to
Adding zero to an expression does not change the expression. So is equal to
Thus, we can rewrite as and we can replace with to get:
Now, we see that the coefficient of is
What is the coefficient of in the expression
We can rewrite the expression as and we can replace with to get: We see that the coefficient of is
What is the coefficient of $n$ in the expression $9h-3-2k?$
|
a
|
$9$ |
|
b
|
$-2$ |
|
c
|
$0$ |
|
d
|
$3$ |
|
e
|
$-3$ |
What is the constant term in the expression $3u+2v+x?$
|
a
|
$3$ |
|
b
|
$x$ |
|
c
|
$0$ |
|
d
|
$2$ |
|
e
|
$1$ |