Synthetic Division Polynomials

Question

p(x)=x^3−3x^2−2x+1 can be computed via synthetic division by filling in for the letters a through g in the table.

1 -3 -2 1

b d f

a c e g

where

? =a

? =b

? =c

? =d

? =e

? =f

? =g

Moreover, p(-2) = ? and can be written as p(x)=(x+2)q(x)+r

where q(x)=? is a quadratic polynomial and r=? is a real number.

Answer 1

1 -3 -2 1 |-2

-2 10 -16

-------------------

1 -5 8 -15

a=1

b=-2

c=-5

d=10

e=8

f=-16

g=-15 --> remainder

p(-2)=-8-12+4+1 = -15

q(x) = x²-5x+8

r = -15