Factor. \( 27 p^{2}-90 p+63 \) \( \square \) Submit

To factor \( 27 p^{2}-90 p+63 \), we start by looking for the greatest common factor (GCF) of the coefficients. The GCF is 9. So, we can pull it out first: \( 9(3p^{2}-10p+7) \) Next, we need to factor the quadratic expression \( 3p^{2}-10p+7 \). We look for two numbers that multiply to \( 3 \cdot 7 = 21 \) and add to \(-10\). These numbers are \(-3\) and \(-7\): Rewrite the quadratic as: \( 9(3p^{2}-3p-7p+7) \) Now, group the terms: \( 9((3p^{2}-3p)-(7p-7)) \) Factoring gives us: \( 9(3p(p-1)-7(p-1)) \) This leads to: \( 9(p-1)(3p-7) \) So the final factored form is: \( 9(p-1)(3p-7) \)