Question

if x-2 and x+ 3 are factors of x^3 ax^2 + bx - 3 find a and b

Answer 1

x-2
x=2
p(2)=(2)^3+a(2)^2+b(2)-3
=8+4a+2b-3
4a+2b+5=0

x+3
x=-3
p(-3)=(-3)^3+a(-3)^2+b(-3)-3
=-27+9a-3b-3
9a-3b-30=0
a=3b+30÷9
a=b+10/3
substitute a in equation 1
4a+2b+5=0
4(b+10/3)+2b+5=0
4b+40/3+2b=-5
4b+40+6b/3=-5
4b+6b+40=-5*3
10b=-15-40
b=-55/10
b=-11/5

a=b+10/3
= (-11/5+10)/3
(-11+50/5)/3
39/15=13/5