Question

Find the greatest common factor of 15x 2 y 3 and -20x 3 yz.

[ ] x [ ] y [ ]

The [ ] are blanks

Answer 1

The greatest common factor is 5x²y. The solution are 5, 2 and 1. Blank 1=5, Blank 2=2 and Blank 3=1.

Explanation:

The given numbers are

`15x^2y^3`

`-20x^3yz`

The factors of given numbers are

`15x^2y^3=3* 5* x* x* y* y* y`

`-20x^3yz=-4* 5* x* x* x* y* z`

The greatest common factor is

`G.C.F=5* x* x* y`

`G.C.F=5x^2y`

Therefore the greatest common factor is 5x²y. The solution are 5, 2 and 1.

Answer 2

The greatest common factor is 5x²

Explanation:

Step 1 : To find the greatest common factor, break down every term of both the polynomials into prime factors

`15\cdot x^(2)\cdot y^3=3* 5* x* x* y* y* y\\-20\cdot x^3\cdot y\cdot z=-1* 2* 2* 5* x* x* x* y* z`

Step 2 : Now find the common factors which are common in both the polynomials

Common factors are : 5 , x and x

Step 3 : To find the greatest common factor find product of all the common factors obtained in the previous step

Greatest Common Factor = 5 × x × x

= 5·x²

So, The blanks will be : [5] x[2] y[0]