Skill: Identify coefficients

Explanation and Free Practice Resources

A coefficient is the numerical factor that multiplies a variable in a term, such as 5 in $5x$ , $-3$ in $-3y$ , or $\frac{1}{2}$ in $\frac{1}{2}a$ ; a variable written alone has an implied coefficient of 1 (or $-1$ when preceded by a minus sign). This understanding distinguishes coefficients from constant terms and supports combining like terms and interpreting equations; symbolic coefficients and more formal polynomial generalizations are beyond this scope.

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Detailed Explanation: Identify coefficients

A coefficient is the number multiplying a variable in a term.

To find a coefficient:

Identify the variable.
Look for the number directly multiplying it.
If no number is written, the coefficient is $1$ .
If a minus sign comes before the variable, the coefficient is $-1$ .
A number without a variable is a constant, not a coefficient.

Consider the expression

6x-4+y-3z+8

Break it into terms:

$6x$ : The coefficient of $x$ is $6$ .
$-4$ : This has no variable, so it is a constant, not a coefficient.
$y$ : This can be written as $1y$ , so the coefficient of $y$ is $1$ .
$-3z$ : The coefficient of $z$ is $-3$ .
$8$ : This has no variable, so it is a constant.

Therefore, the coefficients are:

6,\quad 1,\quad -3

The constants are $-4$ and $8$ .

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Identify Coefficient - Polynomial and Term to Coefficient

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