P(-2) for P(x)=2x^3+2x^2+9

Question

Use the remainder theorem to find P(-2) for P(x)=2x^3+2x^2+9.

 

Give the quotient and remainder for the associated division and the value of P(-2).

Answer 1

P(-2) for P(x)=2x^3+2x^2+9

 

p(-2) =2(-2)³ + 2(-2)²  + 9

         =2(-8) + 2(4) +9

        =-16+8+9

        =-8+9

       =1

so  remainder is 1 while quotient is x+2 

 

Answer 2

(2x³ + 2x²)/(x + 2) = 2x²

 

2x²(x + 2) = 2x³ + 4x²

 

2x³ + 2x² - 2x³ - 4x²  = -2x²

 

(-2x² + 0x)/(x + 2) = -2x

 

-2x(x + 2) = -2x² - 4x

 

-2x² + 0x + 2x² + 4x = 4x

 

(4x + 9)/(x + 2) = 4

 

4(x + 2) = 4x + 8

 

4x + 9 - 4x - 8 = 1

 

2x² - 2x + 4 r 1