Question

How do you factor \[28x - 49\]?

Answer 1

Hint: We use the distributive property of multiplication over subtraction in this question. We take the common number of terms that is a factor of both the terms and bring it outside from both the terms.
Distributive Property: For any three numbers ‘a’, ‘b’ and ‘c’ we can write \[a(b - c) = ab - bc\]
Factor of an equation means that the equation is exactly divisible by that factor. If there is one factor of an equation, then there can be other factors as well which when multiplied to each other give us the original equation.

Complete step by step answer:
We have to find factors of \[28x - 49\] … (1)
We use the distributive property of multiplication over subtraction here to open the value.
We know the distributive property of multiplication over subtraction is given by the formula \[a(b - c) = ab - bc\]
We know we can write the numbers \[28 = 7 \times 4\] and \[49 = 7 \times 7\]
Now substitute the value of numbers as product of their factors in equation (1)
\[ \Rightarrow 28x - 49 = \left[ {(7 \times 4)x - (7 \times 7)} \right]\]
Now we see that 7 is a factor of both the terms in the brackets on right hand side of the equation, so we bring the common factor i.e. 7 outside the bracket and write the remaining factors inside the bracket i.e. by using the distributive property we can collect terms
\[ \Rightarrow 28x - 49 = 7\left[ {(4)x - (7)} \right]\]
So, the bracket on right hand becomes
\[ \Rightarrow 28x - 49 = 7\left[ {4x - 7} \right]\]
So, the terms on the right hand side are factors of the term on the left hand side of the equation.

The factor of the equation \[28x - 49\]is \[7\left( {4x - 7} \right)\] .

Note: Many students make mistakes solving for the value of ‘x’ from the obtained factors i.e. they equate the factors to 0 and write the value of x as \[7/4\]. Keep in mind we do not need the value of ‘x’, we need to simplify the equation and write the equation in factored form i.e. such a form that indicates the numbers or terms that completely divide the equation.