Factor the potynomial. \[ 24 p^{2}-20 p+12 \] \( 24 p^{2}-20 p+12=\square \)

To factor the polynomial \( 24p^{2} - 20p + 12 \), we start by finding the greatest common factor (GCF) of the coefficients. The GCF of 24, 20, and 12 is 4. We can factor out the 4: \[ 24p^{2} - 20p + 12 = 4(6p^{2} - 5p + 3) \] Now, we focus on factoring \( 6p^{2} - 5p + 3 \). We look for two numbers that multiply to \( 6 \times 3 = 18 \) and add to \(-5\). Unfortunately, no such pair exists that is consistent with our integer requirements. Consequently, we can conclude that \( 6p^{2} - 5p + 3 \) is not factorable using integer coefficients. So, the final factored form is: \[ 24p^{2} - 20p + 12 = 4(6p^{2} - 5p + 3) \]