Question

How do you find the GCF for 17xy⁴+51x³y³?

I'm clueless

Answer 1

`17xy⁴+51x³y³`

lets expand each term to its simplest,

`=17x*y*y*y*y+17*3*x*x*x*y*y*y`

Now taking out the common factor,

`=17xy^3(y +3x^2)`

This method isnt practical when it comes to larger terms.
so the basic method is the just find the number of common variables from each term and write them together. same goes for the numerical part.

Answer 2

To find the GCF, find all the common factors that the terms have

Explanation:

First, let's examine the coefficients (17 and 51):

17 goes into 51 3 times (17 times 3 is 51).

`17(xy^4+3x^3y^3) rarr` Use the distributive property to distribute the 17 out of each term.

Next let's look at the x's.

The first term has 1 x, the second term has 3 x's being multiplied together. `x` goes into `x^3` or `x*x*x` 3 times.

`17x(y^4+3x^2y^3) rarr` Divide each term by x

Finally, let's look at the y's.

The first term has 4 y's being multiplied together. The second has 3 y's being multiplied together. `y*y*y*y` divided by `y*y*y` is `y`.

`17xy^3(y+3x^2) rarr` Factor out the `y^3`

The GCF is `17xy^3`. It is all what has been factored out of the two terms; it is what the two share in common.