Question

Statement 1: The polynomial $x^5+2x^4+3x^3+x^2–7x+8$ when divided by x + 1, gives 14 as remainder.

Statement 2: The value of the polynomial $x^5+2x^4+3x^3+x^2–7x+8$ at x = -1 is 14.

• A. Both the statements are true and statement 2 is the correct explanation of statement 1.
• B. Both the statements are true and statement 2 is not the correct explanation of statement 1.
• C. Statement 1 is true but statement 2 is false.
  
• D. Statement 1 is false but statement 2 is true.

Answer 1

The correct option is A Both the statements are true and statement 2 is the correct explanation of statement 1.

Remainder theorem states that a polynomial P(x) of degree greater than or equal to one, when divided by x – a, gives P(a) as the remainder. P(a) should be a polynomial of degree greater than 1 and a can be any real number. So, when $x^5+2x^4+3x^3+x^2–7x+8$ is divided by x +1, the remainder is P(-1) which is 14.