MATH(polynomials)

When g(x)=2x^3+px^2+qx+2 is divided by 2x-1,the quotient is x^2+4x+3 and the remainder is 5.
(a).Find the values of p and q .(計左係p=7,q=2)唔洗計(a)呢條
(b).Hence solve the equation g(x)=5<&l t;<唔識,answer:-3,-1,1/2
(b)
from (a)
g(x)=2x^3+7x^2+2x+2=(x^2+4x+3)(2x-1)+5
g(x)=5
(x^2+4x+3)(2x-1)+5=5
(x^2+4x+3)(2x-1)=0
(x^2+4x+3)=0 or (2x-1)=0
(x+3)(x+1)=0 or x=1/2
so x=-3 or x=-1 or x=1/2

g(x)=5

2x^3+7x^2+2x+2 = 5

(2x - 1) (x^2+4x+3) + 5 = 5

(2x - 1) (x^2+4x+3) =0

(2x - 1) (x+3) (x+1) = 0

x= -3, -1, 1/2