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

Answer:

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

Step-by-step 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.

$12xy \Rightarrow 2\times 2\times 3\times x\times y\\ \\ 28xz\Rightarrow 2\times 2\times 7\times x\times z$

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

So, the GCF will be:  $2\times 2\times x= 4x$

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

$12xy+28xz\\ \\ = 4x(\frac{12xy}{4x}+ \frac{28xz}{4x}) \\ \\ =4x(3y+7z)$

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