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What are the factors of \[18x - 45\]?

Last updated date: 15th Jul 2024
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Hint: Factors are whole numbers that are multiplied to create a new number. The product number is a factor of the original numbers. \[a\] and \[b\]are factors of \[c\] if \[a \times b = c\]. In order to find out the factors of a given number we should use the multiplication table. The given question is in the form of a linear equation with one variable.

Complete step-by-step answer:
A number's factor is defined as a number that divides the original number evenly or precisely. The term factor refers to a whole number that can equally split a larger number. Linear equations are yet another category of "equations." Linear equations can be used to perform any linear calculations that require more than one variable. A linear equation in one variable has the normal/standard form of:
\[ax + b = 0\]
\[x\] is a variable, and \[a\] & \[b\] are constants in this equation which cannot be zero.
We can proceed to calculate the factors \[18x - 45\]of as follows:
With the help of multiplication table, we can find out that is a \[9\] common factor and the equation can be written as:
\[ \Rightarrow 18x - 45 = (9 \times 2x) - (9 \times 5)\]
Taking out the common factor,
\[ \Rightarrow 18x - 45 = 9(2x - 5)\]
Hence the factor is \[9(2x - 5)\].
So, the correct answer is “s \[9(2x - 5)\]”.

Note: Linear equations are equations of degree \[1\]. In the given case, \[x\] has power of \[1\]. Hence it is a linear equation. The geometrical representation of a degree/power one equation is a straight line, which is why it is called a linear equation.
There can be linear equations with more than one variable. E.g. \[ax + by = c\]has two variables \[x\] and \[y\].