Question

[
begin{aligned}
text { let } f(x) &=x^{2}+p x+q
g(x) &=x^{2}+m x+n
end{aligned}
]
( f(x), g(x) ) have a factor ( 18(x+a) )
then
[
begin{array}{c}
f(-a)=(-a)^{2}+p(-a)+q=0
a^{2}-p a+q=0 quad-(1
g(-a)=a^{2}-m a+n=0
end{array}
]
from ( (1)=0 ) ( a^{x}-p a+q=a^{2}-m a+n )
[
begin{array}{c}
m a-p a=n-q
a(m-p)=n-q
a=n-q
end{array}
]
i-p

# f(x ) is the factor of the polynomial x x* and xerxen, prove that MD

Solution