Identify Common Factors: Look for common factors in pairs of terms.We will first look at the terms 9m3 and −18m2 to see if there is a common factor. We can factor out 9m2 from both terms.9m3−18m2=9m2(m−2)
Factor Out Common Factors: Look for common factors in the remaining pair of terms.Now we will look at the terms −2m and +4 to see if there is a common factor. We can factor out −2 from both terms.−2m+4=−2(m−2)
Write Down Findings: Write down what we have found so far.We have found:9m3−18m2=9m2(m−2)−2m+4=−2(m−2)Now we can write the polynomial as a combination of these two factored expressions:9m3−18m2−2m+4=9m2(m−2)−2(m−2)
Factor Out Binomial: Factor out the common binomial factor.We can see that the binomial (m−2) is common in both terms, so we can factor it out.9m3−18m2−2m+4=(m−2)(9m2−2)
Check Quadratic Factor: Check if the quadratic factor can be factored further.The quadratic factor 9m2−2 does not have any common factors and cannot be factored further using integers. Therefore, the factored form of the polynomial is:9m3−18m2−2m+4=(m−2)(9m2−2)