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

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!

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

Suggest Corrections

Similar questions

The polynomial x^{5} + 2 x^{4} + 3 x^{3} + x^{2} - 7 x + 8 when divided by (x + 1) leaves a remainder of 14 .

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

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

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

Statement 1: A polynomial P(x) of degree greater than or equal to one, when divided by x – a, leaves a remainder zero.

Statement 2: x – a is a factor of the polynomial P(x).

Statement 1: The polynomial $P (x) = 4 x^{3} - 3 x^{2} + 5 x - 6$ when divided by $x - 1$ gives zero as the remainder.

Statement 2: $(x - 1)$ is a factor of the polynomial $P (x) = 4 x^{3} - 3 x^{2} + 5 x - 6$ .

Statement 1:

(\sqrt{- 3 + 4 x - x^{2}} + 4)^{2} + (x - 5)^{2}

1 \leq x \leq 3)

36.

Statement 2:

(5, - 4)

(x - 2)^{2} + y^{2} = 1

6

Join BYJU'S Learning Program