If 2x^2-dx+(31-d^2)x+5 has a factor of x - d, what is the value of d if d is an integer?
Hint: $\displaystyle f(d)=2(d)^2-d(d)+(31-d^2)(d)+5=2d^2-d^2+31d-d^2+5=0$
Write in standard form:
$\displaystyle d^3-d^2-31d-5=0$
Now, use the rational roots theorem to see if this cubic has any integral roots.
Small missing step: If x-a is a factor of a polynomial P(x), then P(a) = 0 (Remainder theorem).
Salahuddin
Maths online
That missing step was given in a duplicate post in another forum. I didn't feel it necessary to repeat it, but rather continued the discussion here after he was asked to post in an appropriate forum.