Use long division

Question

P(x) and a divisor d(x) are given Use division to find the quotient Q(x) and the remainder R(x) . Express P(x) in the form P(x) = d(x) * Q(x) + R(x)

P(x)=x^3-125

D(x)=x+5

Fill in the blanks: x^3-125=(x+5)(blank)-blank

Answer 1

P(x) = x^3 -125 = (x-5)(x^2 +5x +25) but

d(x) = x+5, so factoring doesn't work

P(x)/(x+5)

= x^2 -5x+25 = Q(x)

with R(x)=-250