Question

If x^3+lx+m leaves the same remainder 7, when divided by(x-1) or by(x+1).Find l and m.

Answer 1

Step-by-step explanation:

(x-1) ) x³+ lx+ mbl ( x²+x+1

x³- x²

- +

x²+ lx+ m

x²- x

- +

x( l- 1 ) + m

x - 1

- +

x( l -2 ) + ( m-1 )

l = 2, m = 8

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Answer 2

Step-by-step explanation:

do a little synthetic division.

R(x-1) = m+(l+1)

R(x+1) = m-(l+1)

m-(l+1) = m+(l+1)

2(l+1) = 0

l = -1

and m can be anything. So,

f(x) = x^3-x+m

the remainder is always m.