Question

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

Answer 1

Given :- P(x) is a polynomial.

• P(x) divided by (x + 7) has a remainder of 5.
• P(x) divided by (x + 3) has a remainder of (-4).
• P(x) divided by (x - 3) has a remainder of 6.
• P(x) divided by (x - 7) has a remainder of 9.

To Find :- The following values of P(x).

• P(-3) = ?
• P(7) = ?

Answer :-

we know that,

• The Remainder Theorem states that when a polynomial is p(x) is divided by another binomial (x - a), then the remainder will be p(a) .

given that,

• P(x) divided by (x + 3) has a remainder of (-4).

so,

• p(x) divided by (x - a) has a remainder of p(a) .

comparing,

→ x + 3 = x - a

→ a = (-3)

therefore,

→ p(-3) = remainder = (-4) (Ans.)

similarly, given that,

• P(x) divided by (x - 7) has a remainder of 9.

so,

• p(x) divided by (x - a) has a remainder of p(a) .

comparing,

→ x - 7 = x - a

→ a = 7

therefore,

→ p(7) = remainder = 9 (Ans.)

Learn more :-

JEE mains Question :-

https://brainly.in/question/22246812

. Find all the zeroes of the polynomial x4

– 5x3 + 2x2+10x-8, if two of its zeroes are 4 and 1.

https://brainly.in/question/39026698

Answer 2

Step-by-step explanation:

p(x)=x3+4x2-cx+14 ans is =-7