Question

Please help me!!!! Both questions! Find the GCFs:!!

Answer 1

Hi! Hope you're enjoying your day!

First of all, the G.C.F. stands for

Greatest Common Factor

So we need to find the Greatest Common Factor of the polynomials.

And yea, polynomials have Greatest Common Factors as well.

So, let's find all the Greatest Common Factors. :)

First, we have

`\bold{28x^2yz}` and
`\bold{16xy^2}`

What are the common factors of these polynomials?

Well, there are plenty of them, like 2, 2x, y...

What is the Greatest Common factor?

Is it Option A, 12xy?

No, because neither 28 nor 16 is divisible by 12.

So we cross out Option A.

Is it Option B, 8xy?

No, because 28 isn't divisible by 8, and remember, if a number is evenly divisible by another number, then that number is a factor.

Example: 8 is a factor of 16 (16÷8=2); 8 is not a factor of 28, because

28÷8=3.5 (a decimal, not a whole number)

Is it Option C, 4xy?

Yeah, it seems like Option C is the right option.

`\huge\checkmark`Both 28 and 16 are divisible by 4

`\huge\checkmark`Both polynomials have an x and a y in them

`\rule{250}{2}`

Find the GCF:

`\bold{5x^2y^4,\:10x^3y^5, \:and\:15xy^2}`

Once again, is it Option A, 5x^3y^5?

No, because

✘ 5 and 10 aren't divisible by 3

✘ None of the 3 polynomials has a 3y term

In other words, Option A is wrong.

How about Option B?

You should see right off the bat that 5 and 15 aren't divisible by 10.

So now we have 2 options left.

Is it Option C, 5xy²?

Well,

✓All 3 polynomials are divisible by 5

✓ All 3 polynomials have a y² term

✓ All 3 polynomials have an x term.

Hence, the answers are

`\boxed{\boxed{\bold{1. \;Option\;C; 2.\;Option\;C.}}}`

Hope everything is clear.

If you have any questions, please comment.

#LearningIsFun

`\rule{200}{2}`

Answer 2

See below.

Explanation:

28x^2yz and 16xy^2

GCF of 28 and 16: 4

GCF of x^2yz and xy^2: xy

The GCF is 4xy.

5x^2y^4, 10x^3y^5, and 15xy^2

GCF of 5, 10, and 15: 5

GCF of x^2y^4, x^3y^5, and xy^2: xy^2

The GCF is 5xy^2.

-hope it helps