Identify Common Factors: Look for common factors in pairs of terms.We will first look at the pairs of terms to see if there are any common factors that can be factored out.For the first two terms, 8z3 and −6z2, the common factor is 2z2.For the last two terms, −12z and 9, the common factor is 3.
Factor Out Common Factors: Factor out the common factors from each pair.Factor out 2z2 from the first pair and 3 from the second pair.8z3−6z2=2z2(4z−3)−12z+9=−3(4z−3)Notice that we factored out −3 from the second pair to get a common binomial factor of (4z−3).
Rewrite Expression with Factored Pairs: Write the expression with the factored pairs.Now we rewrite the expression using the factored pairs from Step 2.8z3−6z2−12z+9=2z2(4z−3)−3(4z−3)
Factor Out Common Binomial Factor: Factor out the common binomial factor.We can see that (4z−3) is a common factor in both terms.Factor out (4z−3) from the expression.8z3−6z2−12z+9=(2z2−3)(4z−3)