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Factor.\newline12z316z2+3z412z^3 - 16z^2 + 3z - 4

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Q. Factor.\newline12z316z2+3z412z^3 - 16z^2 + 3z - 4
  1. Identify Common Factors: Look for common factors in pairs of terms. We will group the terms into two pairs and look for common factors in each pair. Group 11: 12z312z^3 and 16z2-16z^2. Group 22: 3z3z and 4-4.
  2. Factor Out Common Factors: Factor out the greatest common factor from each group.\newlineFor Group 11, the greatest common factor is 4z24z^2.\newlineFor Group 22, there is no common factor other than 11.\newlineSo we have:\newlineGroup 11: 4z2(3z4)4z^2(3z - 4)\newlineGroup 22: 3z43z - 4
  3. Check Parentheses: Check if the terms in parentheses are the same for both groups.\newlineWe notice that both groups have the same term in parentheses, which is (3z4)(3z - 4).
  4. Factor by Grouping: Factor by grouping.\newlineSince both groups contain the factor (3z4)(3z - 4), we can factor it out:\newline(4z2+1)(3z4)(4z^2 + 1)(3z - 4)