Question

find the value of A and B so that the polynomial x*3+10*2+ax+bis exactly divisible by (x-1) as well as (x-2)​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

a=-37, b=26

Showing factor theorem (with division algorithm)

Division algorithm A=BQ+R is an identity.

x³+10x²+ax+b=(x-1)Q+0

It is an identity. Let's substitute 1.

1+10+a+b=0 therefore a+b=-11.

x³+10x²+ax+b=(x-2)Q+0

Let's subsitute 2.

8+40+2a+b=0 therefore 2a+b=-48.

We have system equation. The pair of solution is (-37, 26).

Therefore, x³+10x²-37x+26.