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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