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Factor.\newline8z36z212z+98z^3 - 6z^2 - 12z + 9

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Q. Factor.\newline8z36z212z+98z^3 - 6z^2 - 12z + 9
  1. Identify Common Factors: Look for common factors in pairs of terms.\newlineWe will first look at the pairs of terms to see if there are any common factors that can be factored out.\newlineFor the first two terms, 8z38z^3 and 6z2-6z^2, the common factor is 2z22z^2.\newlineFor the last two terms, 12z-12z and 99, the common factor is 33.
  2. Factor Out Common Factors: Factor out the common factors from each pair.\newlineFactor out 2z22z^2 from the first pair and 33 from the second pair.\newline8z36z2=2z2(4z3)8z^3 - 6z^2 = 2z^2(4z - 3)\newline12z+9=3(4z3)-12z + 9 = -3(4z - 3)\newlineNotice that we factored out 3-3 from the second pair to get a common binomial factor of (4z3)(4z - 3).
  3. Rewrite Expression with Factored Pairs: Write the expression with the factored pairs.\newlineNow we rewrite the expression using the factored pairs from Step 22.\newline8z36z212z+9=2z2(4z3)3(4z3)8z^3 - 6z^2 - 12z + 9 = 2z^2(4z - 3) - 3(4z - 3)
  4. Factor Out Common Binomial Factor: Factor out the common binomial factor.\newlineWe can see that (4z3)(4z - 3) is a common factor in both terms.\newlineFactor out (4z3)(4z - 3) from the expression.\newline8z36z212z+9=(2z23)(4z3)8z^3 - 6z^2 - 12z + 9 = (2z^2 - 3)(4z - 3)