Question

What are the coefficients of x in the following expression?
\[4x - 3y,\;8 - x + y,\;{y^2}x - y,\;2z - 5xz\].

Answer 1

Hint: Separate the variables whose coefficient is to be found and then find their coefficients.
A coefficient is a number multiplied by a variable and in this question we need to find the coefficient of variable \[x\].
In this question four expressions are given so we will first separate the variable \[x\] from the expressions and then we will find their coefficients.

Complete step by step answer:
$\Rightarrow$ Given the expression \[4x - 3y\]
Here the expression contains both the variables \[x\] and \[y\], since we need to find the coefficients of variable \[x\] so we will separate them, hence we get \[ = 4x\].
Hence the coefficient of the variable \[x\] is 4.

$\Rightarrow$ Now for the expression \[8 - x + y\]
Here the expression contains both the variable \[x\], \[y\] and a constant 8, since we need to find the coefficients of variable \[x\] so we will separate them, hence we get \[ = - x\]
Hence the coefficient of the variable \[x\] is -1.

$\Rightarrow$ Now in the expression \[{y^2}x - y\]
Here the expression contains both the variable\[x\] and \[y\], since we need to find the coefficients of variable \[x\] so we will separate them, hence we get \[ = {y^2}\]
Hence the coefficient of the variable \[x\] is \[{y^2}x\].

$\Rightarrow$ In the expression \[2z - 5xz\]
Here the expression contains both the variable \[x\] and \[z\], since we need to find the coefficients of variable \[x\] so we will separate them, hence we get \[ = - 5xz\]
Hence the coefficient of the variable \[x\] is \[ - 5z\].

Note: An algebraic expression is a mathematical phrase and it contains integral, fractional constants and variables and operators. These algebraic expressions are expressed in terms of term, factor and the coefficient. If there is no numerical factor in the term then the coefficient is taken as +1.