Question
Factor the following polynomial.
3 x left parenthesis y minus 3 right parenthesis plus 7 left parenthesis y minus 3 right parenthesis
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Part 1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
3 x left parenthesis y minus 3 right parenthesis plus 7 left parenthesis y minus 3 right parenthesis equals nothing
(Factor completely.)
B.
The polynomial has no common factor other than 1.
3 x left parenthesis y minus 3 right parenthesis plus 7 left parenthesis y minus 3 right parenthesis
Question content area bottom
Part 1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
3 x left parenthesis y minus 3 right parenthesis plus 7 left parenthesis y minus 3 right parenthesis equals nothing
(Factor completely.)
B.
The polynomial has no common factor other than 1.
Answers
GPT-4o mini
To factor the given polynomial \(3x(y - 3) + 7(y - 3)\), we can identify a common factor in both terms.
Both terms include the factor \((y - 3)\). Therefore, we can factor \((y - 3)\) out:
\[
3x(y - 3) + 7(y - 3) = (y - 3)(3x + 7)
\]
So the polynomial factored completely is:
\((y - 3)(3x + 7)\)
The correct choice is:
A. \(3 x (y - 3) + 7 (y - 3) = (y - 3)(3x + 7)\) (Factor completely.)
Both terms include the factor \((y - 3)\). Therefore, we can factor \((y - 3)\) out:
\[
3x(y - 3) + 7(y - 3) = (y - 3)(3x + 7)
\]
So the polynomial factored completely is:
\((y - 3)(3x + 7)\)
The correct choice is:
A. \(3 x (y - 3) + 7 (y - 3) = (y - 3)(3x + 7)\) (Factor completely.)