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

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

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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Both the statements are true and statement 2 is not the correct explanation of statement 1.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Statement 1 is true but statement 2 is false.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Statement 1 is false but statement 2 is true.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

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 is any real number. So, when ${x}^{5}+ 2{x}^{4}+ 3{x}^{3}+ {x}^{2}– 7x + 8$ is divided by x +1, the remainder is 14 which is same as P(-1).

Suggest Corrections

Similar questions

Q. Statement 1: The polynomial

x^{5} + 2 x^{4} + 3 x^{3} + x^{2} - 7 x + 8

when divided by x + 1, gives 14 as remainder.

Statement 2: The value of the polynomial

x^{5} + 2 x^{4} + 3 x^{3} + x^{2} - 7 x + 8

at x = -1 is 14.

Q. A polynomial p(x) is divided by (2x - 1). The quotient and remainder obtained are

(7 x^{2} + x + 5)

and 4 respectively. Find p(x).
OR
Find the quotient and remainder using synthetic division.

(3 x^{3} - 2 x^{2} + 7 x - 5) \div (x + 3)

The polynomial $x^{4} - {2 x}^{3} + {3 x}^{2} - a x + b$ when divided by $x + 1$ and $x - 1$ gives remainders 19 and 5 respectively. Find the remainder when the polynomial is divided by $x - 3$ . [3 MARKS]

Q. Divide:

2 x^{5} - 7 x^{4} - 2 x^{3} + 18 x^{2} - 3 x - 8

x^{3} - 2 x^{2} + 1

Q. When the polynomial

x^{6} - 2 x^{5} + 3 x^{2} + 4

is divided by

x + 1

the remainder is :

Join BYJU'S Learning Program

Statement 1: The value of the polynomial \({x}^{5} + 2{x}^{4} + 3{x}^{3}+ {x}^{2}– 7x + 8\) at x = -1 is 14. Statement 2: The polynomial \({x}^{5} + 2{x}^{4} + 3{x}^{3}+ {x}^{2}– 7x + 8\) when divided by x + 1, gives 14 as remainder.

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

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