Question

if two polynomials p(x)= x³-3x²+7x+c and q(x)=x²-5x+b are divided by (x-2), the remainders are 15 and -13 respectively, then the polynomial 2x²+bx+c can be factored as

a) (x+1)(2x-5)
b) (x-1)(2x-5)
c) (x+1)(2x+5)
d) (x-1)(2x+5)

Answer 1

g (x)=0
x-2=0
x=2

p (2)=2^3-3^2+7×2+c=15
8-12+14+c=15
10+c=15
c=5

q (2)=2^2-5×2+b=-13
b=7


equ.a & b
2x^2-7x+5
2x^2-2x-5x+5
2x (x-1)-5 (x-1)
(x-1)(2x-5)