Find the greatest common factor of the expressions below, if one exists. 40 ( 7 − y ) 5 , 50 ( 7 − y ) 4 40 ( 7 - y ) ^ { 5 } , 50 ( 7 - y ) ^ { 4 } 40 ( 7 − y ) 5 , 50 ( 7 − y ) 4 A) 40 ( 7 − y ) 4 40 ( 7 - y ) ^ { 4 } 40 ( 7 − y ) 4 B) 5 ( 7 − y ) 10 5 ( 7 - y ) ^ { 10 } 5 ( 7 − y ) 10 C) 10 ( 7 − y ) 4 10 ( 7 - y ) ^ { 4 } 10 ( 7 − y ) 4 D) 4 ( 7 − y ) 5 4 ( 7 - y ) ^ { 5 } 4 ( 7 − y ) 5 E) No greatest common monomial factor exists.

Question

Find the greatest common factor of the expressions below, if one exists.   40 ( 7 − y )  5 , 50 ( 7 − y )  4 40 ( 7 - y )  ^ { 5 } , 50 ( 7 - y )  ^ { 4 } 40 ( 7 − y )  5 , 50 ( 7 − y )  4 A)    40 ( 7 − y )  4 40 ( 7 - y )  ^ { 4 } 40 ( 7 − y )  4 B)    5 ( 7 − y )  10 5 ( 7 - y )  ^ { 10 } 5 ( 7 − y )  10 C)    10 ( 7 − y )  4 10 ( 7 - y )  ^ { 4 } 10 ( 7 − y )  4 D)    4 ( 7 − y )  5 4 ( 7 - y )  ^ { 5 } 4 ( 7 − y )  5 E) No greatest common monomial factor exists.

Andre Clemons · Accepted Answer

Final Answer : C, Explanation :  The common factor is $10 (7-y)^4$. This can be found by taking the greatest common factor of the coefficients (which is 10) and the greatest power of the common factor $(7-y)$, which is 4. Therefore, the answer is $\boxed{	extbf{(C)}}$.

Find the greatest common factor of the expressions below, if one exists. $40 ( 7 - y ) ^ { 5 } , 50 ( 7 - y ) ^ { 4 }$

A) $40 ( 7 - y ) ^ { 4 }$
B) $5 ( 7 - y ) ^ { 10 }$
C) $10 ( 7 - y ) ^ { 4 }$
D) $4 ( 7 - y ) ^ { 5 }$
E) No greatest common monomial factor exists.

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