Question

Find the value of c that (x+2) is a factor of the polynomial p(x)
p(x)=x^4-x^3+cx^2+3x-2

Answer 1

comparing (x+2) with (x-a) we get a=-2

Using factor theorem

p(x)=0

p(-2)=0

(-2)⁴-(-2)³+c×(-2)²+3×-2-2=0

-16+8+4c+12=0

4+4c=0

4c=-4

c=-4/4

c=-1