Let p(x)=2x^3-8x^2-23x+63. Using synthetic division

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1.) p(5)

2.) p(-2i)

3.) p(2+i)

Apr 8th, 2015

5    2    -8     -23        63

           10      10      - 65


     2      2     -13        - 2                        p(5) = - 2 


-2i         2     -8             -23               63

                    -4i           -8+16i        32+62i

             2      -8-4i     -31+16i        95+62i                        p(-2i) = 95 + 62i
 

2+i         2          -8             -23               63

                       4+2i            -10          -66-33i

              2      -4+2i            -33          -3-33i                        p(2+i) = -3 -33i
Apr 8th, 2015

On #2 how did you come up with -8+16i when you multiplied (-8-4i)(-2i)? I thought that it would be -8+8i.

Apr 8th, 2015

(-8-4i)(-2i) = (-8)(-2i) + (-4i)(-2i) = 16i + 8i^2 = 16i -8

Apr 8th, 2015

Okay, I understand now, thank you.

Apr 8th, 2015

You are welcome.

Apr 8th, 2015

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