Question

Please someone help asap!!!

Answer 1

Answer:

True

Step-by-step explanation:

Construct a second-degree polynomial q(x)=ex^2+fx+g

f(x)/(x+1) = q(x) + (2/(x+1))

= ((x+1) * q(x) + 2) / (x+1)

so f(x) = (x+1) * q(x) + 2

substitute our q(x):

f(x) = (x+1)(ex^2+fx+g) + 2

= ex^3 + fx^2 + gx + ex^2 + fx + g + 2

= ex^3 + (e+f)x^2 + (f+g)x + (g + 2)

this still equals ax^3+bx^2+cx+d so by like terms we have

e = a

e + f = b

f + g = c

g + 2 = d

This means we can find an infinite number of solutions that satisfy the property.