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Section 1-5 : Factoring Polynomials

For problems 1 – 4 factor out the greatest common factor from each polynomial.

  1. \(6{x^7} + 3{x^4} - 9{x^3}\) Solution
  2. \({a^3}{b^8} - 7{a^{10}}{b^4} + 2{a^5}{b^2}\) Solution
  3. \(2x{\left( {{x^2} + 1} \right)^3} - 16{\left( {{x^2} + 1} \right)^5}\) Solution
  4. \({x^2}\left( {2 - 6x} \right) + 4x\left( {4 - 12x} \right)\) Solution

For problems 5 & 6 factor each of the following by grouping.

  1. \(7x + 7{x^3} + {x^4} + {x^6}\) Solution
  2. \(18x + 33 - 6{x^4} - 11{x^3}\) Solution

For problems 7 – 15 factor each of the following.

  1. \({x^2} - 2x - 8\) Solution
  2. \({z^2} - 10z + 21\) Solution
  3. \({y^2} + 16y + 60\) Solution
  4. \(5{x^2} + 14x - 3\) Solution
  5. \(6{t^2} - 19t - 7\) Solution
  6. \(4{z^2} + 19z + 12\) Solution
  7. \({x^2} + 14x + 49\) Solution
  8. \(4{w^2} - 25\) Solution
  9. \(81{x^2} - 36x + 4\) Solution

For problems 16 – 18 factor each of the following.

  1. \({x^6} + 3{x^3} - 4\) Solution
  2. \(3{z^5} - 17{z^4} - 28{z^3}\) Solution
  3. \(2{x^{14}} - 512{x^6}\) Solution