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Quiz 9
Factor the following polynomials using integers. If it is not possible, state so.

note: all these can be solved with the quadratic formula; I chose not to use it when possible but it will always work!
1.) Solve x2+1=0.
Solution: Subtract 1 to get x2=1. Now take square roots of each side to get x=±1=±i.

2.) Solve x2+2x+1=0.
Solution: The left-hand side factors to give us (x+1)(x+1)=0. This yields two equations (which happen to be the same): x+1=0 and x+1=0. Hence the only solution is x=1 (which appears twice).

3.) Solve x216=0.
Solution: Add 16 to both sides to get x2=16. Now take the square root of each side to get x=±16=±4.

4.) Solve 5x23x+2=0.
Solution: For this we use the quadratic formula with a=5, b=3, and c=2 to get x=(3)±(3)24(5)(2)25=3±94010=3±3110=3±31i10=310±3110i.

5.)Solve 3x2+x+4=0.
Solution: The left-hand side factors and we get (x+1)(3x4)=0, hence the solution is x=1,43.