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Factor.\newline9m318m22m+49m^3 - 18m^2 - 2m + 4

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Q. Factor.\newline9m318m22m+49m^3 - 18m^2 - 2m + 4
  1. Identify Common Factors: Look for common factors in pairs of terms.\newlineWe will first look at the terms 9m39m^3 and 18m2-18m^2 to see if there is a common factor. We can factor out 9m29m^2 from both terms.\newline9m318m2=9m2(m2)9m^3 - 18m^2 = 9m^2(m - 2)
  2. Factor Out Common Factors: Look for common factors in the remaining pair of terms.\newlineNow we will look at the terms 2m-2m and +4+4 to see if there is a common factor. We can factor out 2-2 from both terms.\newline2m+4=2(m2)-2m + 4 = -2(m - 2)
  3. Write Down Findings: Write down what we have found so far.\newlineWe have found:\newline9m318m2=9m2(m2)9m^3 - 18m^2 = 9m^2(m - 2)\newline2m+4=2(m2)-2m + 4 = -2(m - 2)\newlineNow we can write the polynomial as a combination of these two factored expressions:\newline9m318m22m+4=9m2(m2)2(m2)9m^3 - 18m^2 - 2m + 4 = 9m^2(m - 2) - 2(m - 2)
  4. Factor Out Binomial: Factor out the common binomial factor.\newlineWe can see that the binomial (m2)(m - 2) is common in both terms, so we can factor it out.\newline9m318m22m+4=(m2)(9m22)9m^3 - 18m^2 - 2m + 4 = (m - 2)(9m^2 - 2)
  5. Check Quadratic Factor: Check if the quadratic factor can be factored further.\newlineThe quadratic factor 9m229m^2 - 2 does not have any common factors and cannot be factored further using integers. Therefore, the factored form of the polynomial is:\newline9m318m22m+4=(m2)(9m22)9m^3 - 18m^2 - 2m + 4 = (m - 2)(9m^2 - 2)