Factor the Expression: 3x + 12y² + 9y⁴ Step by Step

Note that in the given expression there are two terms that can have a common factor taken out for the letters:

$12y^2,\hspace{4pt}9y^4$ however the third term:$3x$
which is completely different from the two terms mentioned above (which depend on y) since it does not depend on y, it does not allow taking out a common factor for the letters in all three terms together,

$$meaning - a common factor cannot be taken out for the letters,

Therefore, we will take out the largest common factor for the numbers 3, 9, 12, which is clearly the number 3 since it is prime and is a factor of both other numbers:

$3x+12y^2+9y^4 =3(x+4y^2+3y^4)$

when after taking out the common factor outside the parentheses, we will look at each term before taking out the common factor separately, asking ourselves: "By how much did we multiply the common factor to get the current term?" and we will fill in the missing part inside the parentheses while making sure that the sign of the term we completed inside the parentheses when multiplied by the sign of the term we took outside the parentheses gives the original term's sign, it is recommended to verify that the factoring was done correctly by opening the parentheses, performing the multiplications and confirming that we indeed get the expression before factoring.

Therefore, the correct answer is answer A.