Help Please!!!

Hello SpongeBobRules24! I am mentally lazy so I'm just gonna manually solve for a, b, c

Let us subsitute:

 

P(1) = a + b + c = 1

P(2) = 4a + 2b + c = 2

P(3) = 9a + 3b + c = 4

 

We have:

(1) a + b + c = 1

(2) 4a + 2b + c = 2

(3) 9a + 3b + c = 4

 

We multiply (2) by 2, and we keep (3)

(1) a + b + c = 4

(2) 8a + 4b  + 2c = 4

(3) 9a + 3b + c = 4

 

(2) - (3)

-a + b + c = 0

a = b + c

 

Substitute that into (1)

2a = 1

a = 1/2

 

Let's go back to the original equations:

(1) a + b + c = 1

(2) 4a + 2b + c = 2

(3) 9a + 3b + c = 4

 

Substitute a:

(1) b + c = (1/2)

(2) 2b + c = 0

(3) 3b + c = -(1/2)

 

We do (3) - (2):

b = -(1/2)

 

We plug that into (1)

c = 1

 

a - b - c = (1/2) - -(1/2) - 1

 

Which evaluates to \(\boxed{0}\)