Question

How do you factor $28x – 49$?

Answer 1

Hint: First notice the common factor among 28 and 49. Then, we will take the common factor out of both like we do in reverse of distributive property.

Complete step by step answer:
We have two terms; one is $28x$ and -49.
We will first find the prime factorization of both 28 and 49.
$ \Rightarrow 28 = 2 \times 2 \times 7$
$ \Rightarrow 49 = 7 \times 7$
We can see that both the 28 and 49 have 7 common in them. Let us take out this 7 out of both of them, we can write the given expression as following:-
$ \Rightarrow $ 28x – 49 = 7(4x) – 7(7)
Now, taking 7 common out of both of them, we will write the given expression as following:-
$ \Rightarrow $ 28x – 49 = 7 (4x – 7)
Thus, we have got our factors as 7 and 4x – 7.

Note: Alternate way to do the same question. Let us do that as follows:-
We are given that we need to find the factors of 28x – 49. We can observe that if we put $x = \dfrac{7}{4}$ in the given equation, we will get 0. So, $x - \dfrac{7}{4}$ must be a factor of the equation 28x – 49.
Now, we will divide the given equation by $x - \dfrac{7}{4}$ to obtain:-
$ \Rightarrow x - \dfrac{7}{4})\overline {28x - 49} $
Now, we will multiply the divisor by 28 to get:-
$ \Rightarrow x - \dfrac{7}{4})\overline {28x - 49} (28$
                     $\underline {28x - 49} $
                                0
Thus, we have our factors as 28 and $x - \dfrac{7}{4}$. By multiplying them, we get the required answer.
The students must note that we are basically just doing the reverse of distributive property. In distributive property, we have a (b + c) = ab + ac
So, we just did the reverse of it. Putting a = 7, b = 4x and c = -7, we get the same result as we got above in the solution that 28 x – 49 = 7 (4x – 7).