Would this be correct?
Factpr completley:
y^3-12y^2+36y
y(y^2-12y+36)
y(y-6)^2
yes. Nicely done!
Thank You, I am just making sure before I turn this in.
Is this answer right to this problem: y^3-12y^2 +35y =y(y-7)(y+5)
Yes, that is correct. To factor completely, you can follow these steps:
1. Look for any common factors in the expression. In this case, both terms have a common factor of y, so you can factor it out: y(y^2-12y+36).
2. Now, focus on factoring the quadratic expression within the parentheses, y^2-12y+36. This can be factored further by looking for two numbers that multiply to give 36 and add up to -12 (the coefficient of the middle term).
3. In this case, the numbers -6 and -6 fulfill the requirement because -6 * -6 = 36 and -6 + -6 = -12.
4. Therefore, you can write the quadratic expression as a perfect square: (y-6)^2.
5. Putting it all together, you have y(y-6)^2 as the completely factored form of the original expression, y^3-12y^2+36y.