factor

Question

p^2-6-q(p^2-6)^2

Answer 1

To factor the expression \( p^2 - 6 - q(p^2 - 6)^2 \), let's start by introducing a substitution to simplify our calculations. Let:

\[ x = p^2 - 6. \]

Now, we can rewrite the expression as:

\[ x - qx^2. \]

Next, we can factor this expression:

\[ x(1 - qx). \]

Now, substituting back \( x = p^2 - 6 \), we have:

\[ (p^2 - 6)(1 - q(p^2 - 6)). \]

Thus, the factored form of the original expression \( p^2 - 6 - q(p^2 - 6)^2 \) is:

\[ (p^2 - 6)(1 - q(p^2 - 6)). \]