P (x) P (x) P, (, x,) is a polynomial. P (x) P (x) P, (, x,) divided by (x+7) (x+7) (, x, plus, 7,) has a remainder of 555. P (x) P (x) P, (, x,) divided by (x+3) (x+3) (, x, plus, 3,) has a remainder of - 4-4minus, 4. P (x) P (x) P, (, x,) divided by (x-3) (x-3) (, x, minus, 3,) has a remainder of 666. P (x) P (x) P, (, x,) divided by (x-7) (x-7) (, x, minus, 7,) has a remainder of 999. Find the following values of P (x) P (x) P, (, x,). P (-3) = P (-3) = P, (, minus, 3,), equals P (7) = P (7) = P, (, 7,), equals

P (-3) = -4

P (7) = 9

Step-by-step explanation:

Consider P (x) is a polynomial.

According to the remainder theorem, if a polynomial, P (x), is divided by a linear polynomial (x - c), then the remainder of that division will be equivalent to f (c).

Using the given information and remainder theorem we conclude,

If P (x) is divided by (x+7), then remainder is 5.

⇒ P (-7) = 5

If P (x) is divided by (x+3), then remainder is - 4.

⇒ P (-3) = -4

If P (x) is divided by (x-3), then remainder is 6.

⇒ P (3) = 6

If P (x) is divided by (x-7), then remainder is 9.

⇒ P (7) = 9

Therefore, the required values are P (-3) = -4 and P (7) = 9.