Question

1.What is the greatest common factor of the polynomial's terms?

Answer 1

Step-by-step explanation:

Write the prime factorization of each term:

9r⁵s = 3²·r⁵·s

6r⁴s² = 2·3·r⁴·s²

12r²s = 2²·3·r²·s

The greatest common factor is the product of the common factors at the lowest exponents.

All three terms are multiples of 3, r, and s.

The lowest exponent of 3 is 1.  The lowest exponent of r is 2.  The lowest exponent of s is 1.

GCF = 3r²s

Factor from the polynomial.

9r⁵s + 6r⁴s² − 12r²s

3r²s (3r³ + 2r²s − 4)

Answer 2

Answer:

(3) (r^2) (s) ( 3r^3 + 2r^2s - 4)

Step-by-step explanation:

For clarity please use " ^ " to indicate exponentiation:

9r5s + 6r4s2 − 12r2s  =>  9r5s + 6r^4s^2 − 12r^2s

Next, look at the numerica coefficients 9, 6 and -12.  What is the largest divisor that goes into each evenly?  3.  

Similarly, ask yourself what the largest possible r and s factors divide into 9r5s + 6r^4s^2 − 12r^2s evenly:    r^2 and s.

Then 9r5s + 6r^4s^2 − 12r^2s = (3) ( 3r^5s + 2r^4s^2 - 4r^2s )

Factoring out r^2:                      (3) (r^2) (3r^3s + 2r^2s^2 - 4s )

Factoring out s:                           (3) (r^2) (s) ( 3r^3 + 2r^2s - 4)