Factor completely. \( 30 q^{3}-40 q^{2}+21 q-28 \)

To factor the polynomial \( 30 q^{3}-40 q^{2}+21 q-28 \) completely, we can first look for any common factors in pairs of terms. Let's group it as follows: 1. Group: \( (30q^3 - 40q^2) + (21q - 28) \) 2. Factor out the common factors in each group: - From the first group, factor out \( 10q^2 \): \( 10q^2(3q - 4) \) - From the second group, factor out \( 7 \): \( 7(3q - 4) \) 3. Now we have: \( 10q^2(3q - 4) + 7(3q - 4) \) 4. Notice that \( (3q - 4) \) is a common factor: \( (3q - 4)(10q^2 + 7) \) Thus, the complete factorization of the polynomial is: \[ (3q - 4)(10q^2 + 7) \]