1.What is the greatest common factor of the polynomial’s terms? 9r5s + 6r4s2 − 12r2s 2.Factor out the GCF. Pl

Question

1.What is the greatest common factor of the polynomial’s terms?
9r5s + 6r4s2 − 12r2s

2.Factor out the GCF.

Please help I need help with number two I know number one is 3r^2s • (3r^3 + 2r^2s – 4)

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Sarah 1 week 2021-10-08T00:57:15+00:00 2 Answers 0

Answers ( )

    0
    2021-10-08T00:58:58+00:00

    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)

    0
    2021-10-08T00:59:02+00:00

    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)

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