Question

Find the remainder when x3 - 5x2 + 10x - 15 is divided by each binomial.
a. x - 1
b. x + 3
c. x - 5
d. x +2

Answer 1

here let f(x)=x3 - 5x2 + 10x - 15
now for a
we need to find f(1)
f(1)=1-5+10-15=-9(remainder when the above expression is divided by x-1)
for the rest find f(-3),f(5) and f(-2) respectively

Answer 2

thank you :)

Answer 3

You get the same answer if you do synthetic division for each factor:
E.g. x-1=0, x=1 or k=1
1 )1 -5 10 -15
1 -4 6
-4 6 -9 Add the 2 rows above, -9 is the remainder.

Answer 4

thank you :) this makes more sense now