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

when x-1=0, when x+2=0,

then x=1. then x= -2

(1)3+10(2)+a(1)+b. =. (-2)3+10(2)+a(-2)+b

3+20+a+b. =. -6+20-2a+b

23+a+b. =. 14-2a+b

a+b+2a-b. =. 14-23

3a. =. -9

a. =. -9/3

a. =. -3

* Now, putting the value of a in the polynomial.

p(x)= x3+10(2)+ax+b. {when x=1}

p(1)=. 1(3)+10(2)+(-3)(1)+b

3+20-3+b

23-3+b

20+b

[b = -20]. and [a = -3]