For the Polynomial -9y^4-6y^2+12y

Question

A) Factor out -3y

B) Factor out 3y

Any help will be greatly appreciated.

Answer 1

If you remove "-3y" from "-9y⁴", you have "3y³" (because "-3y" times "3y³" equals "-9y⁴")

If you remove "-3y" from "-6y²", you have "2y" (because "-3y" times "2y" equals "-6y²")

If you remove "-3y" from "12y", you have "-4" (because "-3y" times "-4" equals "12y")

So the result is: (-3y)(3y³ + 2y - 4)

Can you do question B in the same way?

Answer 2

A) For factoring, it can be helpful to think that you are dividing the polynomial by whichever term is the factor, in this case the -3y and 3y. While factoring out negatives, be sure to pay attention to the sign changes too.

Factoring -3y from -9y⁴ results in -3y(3y³)

The next terms can be done similarly to result in -3y(3y³+2y-4)

B) This answer is similar to A, however the signs of each of the terms are opposite.

3y(-3y³-2y+4)