Question

Find the complete factorization of the expression. 12xy + 28xz A) 4yz(10x) B) 4yz(3x + 7x) C) 4x(3y + 7z) D) 4(3xy + 7yz)

Answer 1

The correct option is: C) 4x(3y + 7z)

Explanation:

Given expression is:
`12xy+28xz`

First we need to find the GCF(Greatest common factor) of
`12xy` and
`28xz` and then we will factor out that GCF.

`12xy \Rightarrow 2* 2* 3* x* y\\ \\ 28xz\Rightarrow 2* 2* 7* x* z`

We can see that the common factors are:
`2,2, x`

So, the GCF will be:
`2* 2* x= 4x`

Now factoring out
`4x` from the given expression, we will get.....

`12xy+28xz\\ \\ = 4x((12xy)/(4x)+ (28xz)/(4x)) \\ \\ =4x(3y+7z)`

So, the complete factorization will be:
`4x(3y+7z)`