Expression: -36y⁹-12y⁷

Question

GCF: □
Factored form: □

Answer 1

To factor the expression \(-36y^9 - 12y^7\), we need to find the greatest common factor (GCF) of the coefficients and the lowest power of \(y\).

1. Finding the GCF of the coefficients:

   • The coefficients are -36 and -12.
   • The GCF of 36 and 12 is 12. Since we consider the negative sign, the GCF is -12.

2. Finding the GCF of the \(y\) terms:

   • The \(y\) terms are \(y^9\) and \(y^7\).
   • The lowest power of \(y\) is \(y^7\).

3. Combining the GCFs:

   • Therefore, the overall GCF of the expression is \(-12y^7\).

Now we can factor the original expression:

\[ -36y^9 - 12y^7 = -12y^7(3y^2 + 1) \]

So, we have:

• GCF: \(-12y^7\)
• Factored form: \(-12y^7(3y^2 + 1)\)