When dividing the expression, find p

Question

When dividing the expression         by   , the remainder is  . Find the value of .

Answer 1

The remainder is simply the value of the function when the root is input for x.

1. Since our factor is x-2, our root would be x = 2.
2. We will substitute in 2 for x and set the function equal the -9 (the remainder).

2(2)³-7(2)²+p(2)+3 = -9

2(8)-7(4)+2p+3 = -9

16-28+2p+3 = -9

-9+2p = -9

3. Solve for p.

-9 + 2p = -9

+9 +9

2p = 0

p = 0

Therefore, the resulting function when p = 0 would be:

2x³ - 7x² +3

Answer 2

p=-8

7x^2 -8x + 3 = (x-2)(7x+6) +9

divide x-2 into 7x^2 -8x +3, gives 7x+6 with remainder -9