Factor the greatest common factor: −4y2 + 12y − 16. −1(4y2 − 12y + 16) −4y(y2 − 3y + 4) −4(y2 − 3y + 4) −4(y2 + 3y − 4)

To factor the greatest common factor of the expression $-4y^2 + 12y - 16$, let's go through the following steps:

1. Break Down the Problem

We need to factor the given quadratic expression $-4y^2 + 12y - 16$.

2. Relevant Concepts

The first step in factoring is to identify the greatest common factor (GCF) of the polynomial terms.

3. Analysis and Detail

1. Identify the coefficients of each term:

   • For $-4y^2$, the coefficient is $-4$.
   • For $12y$, the coefficient is $12$.
   • For $-16$, the coefficient is $-16$.

2. Determine the GCF of $-4$, $12$, and $-16$:

   • The GCF is $4$.

3. Factor out the GCF from the expression: $-4(y^2 - 3y + 4)$ So, the expression can be rewritten as $-4(y^2 - 3y + 4)$.

4. Verify and Summarize

Now let's verify our factoring by distributing: $-4(y^2 - 3y + 4) = -4y^2 + 12y - 16$ This confirms that our factoring is correct.

Final Answer

The factored form with the greatest common factor is: $-4(y^2 - 3y + 4)$