Question

Find the value of a and b so that the polynomial x³+10x²+ax+b is exactly divisible by x-1 and x+2

Answer 1

Answer:

a=31 b=-42

Step-by-step explanation:

if x=1as x-1 is a factor of the polynomial

substitute it in the polynomial

then the equation is

a+b=-11 (1)

if x=-2 as x+2is the factor of the polynomial substitute it in the polynomial

then the equation is

-2a+b=-42(2)

by adding (1) and (2)

we get a=31

substitute a=31 in either

(1) or (2)

therefore we get b=-42