Question

find the values of A and B so that the polynomial x cube minus 10 X square + a x + b is exactly divisible by x minus 1 as well as x-2​

Answer 1

HEY FRIEND HERE YOUR ANSWER

Factor theorem state that p(x) = 0

x = 1,2

p(x) = x³-10x²+ax+b

0 =1-10+a+b

0=-9+a+b.............(1)

0=2³-10(2)²+a(2)+b

0=8-40+2a+b

0=-32+2a+b.........(2)

Minus equ (1) and (2)

-9+a+b -(-32+2a+b)=0

23-a=0

a=23

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keep value in equ 1

0=-9+23+b

b=-14

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So the value of (A,B) is (23,-14)

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THANK YOU

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