Question

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

Answer 1

P(-3)=-4

P(7) = 9

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.