Question

Factorize\[9b - 12x\]
A. \[2\left( {3b + 4x} \right)\]
B. \[3\left( {b - 4x} \right)\]
C. \[3\left( {3b - 4x} \right)\]
D. \[2\left( {3b - x} \right)\]

Answer 1

Hint:Separate the common terms from the given expression and write it in the multiple forms.

Factorization is the method of writing mathematical numbers or the equations in product form and when they are multiplied together we get the original number.

In this question there are two terms in the given expression so find terms which are common between both the terms so that when they are multiplied together original expression is obtained.

Complete step by step solution:
Given the expression whose factor is to be find is\[9b - 12x\]

We can see the given expression contains two terms which are in the subtraction form, now in the given expression we will find the common term from the two terms which are \[9b\]and \[ - 12x\]

Here the variable in the first term is \[b\]and \[x\]in the second term so we cannot take anything common between them but we can see their coefficient are in the multiple of 3, so

we can take 3 as common between them, hence we can write
\[9b - 12x = \left( 3 \right)\left( {3b - 4x} \right)\]

Therefore we get the factors of the expression \[9b - 12x\]as \[3\left( {3b - 4x} \right)\]

Option C is the correct answer.

Note:It is interesting to note that whenever an expression is split into their factors, if we multiply those factors together we will get the expression whose factors were found, this method is used to verify whether the factor for the expression is correct or not.
To verify this, if we multiply the obtained multiple together we get \[3\left( {3b - 4x} \right) = 9b - 12x\],
hence we can say the obtained answer was correct.