Answer

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**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).

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