Question

Find a degree 3 polynomial P such that P(−1) = −3, P(0) =−2, P(1) = −1, and P(2) = 6.

Answer 1

Explanation:

let polynomial P(x)=ax³+bx²+cx+d

-3=-a+b-c+d

-2=d

-1=a+b+c+d

-1=a+b+c-2

a+b+c=1

-3=-a+b-c-2

a-b+c=1

a+b+c-(a-b+c)=1-1=0

2b=0

b=0

so a+c=1

6=8a+4b+2c+d

6=8a+4b+2c-2

8a+4b+2c=8

4a+2b+c=4

or 4a+0+c=4

4a+c=4

a+c=1

subtract

3a=3

a=1

1+c=1

c=0

reqd .P(x)=1x³-2=x³-2