Question

If p(x)=xcube+3xsq.-5x+8is divided by the following, then find the remainder with the help of reminder theorem. (1).x+1.​

Answer 1

Step-by-step explanation:

Given:

› p(x) = x³ + 3x² - 5x + 8

› p(x) ÷ (x + 1)

To find:

› Remainder using remainder theorem.

Solution:

Remainder theorem:

• When a polynomial p(x) is divided by (x - a), the remainder of p(x) is p(a).

⇒ (x + 1) = 0

• x = -1

∴, x³ + 3x² - 5x + 8

=> (-1)³ + 3(-1)² - 5(-1) + 8

=> -1 + 3(1) - 5(-1) + 8

=> -1 + 3 + 5 + 8

=> -1 + 16

∴ 15

∴ The remainder is 15.

Answer 2

Step-by-step explanation:

Given:

› p(x) = x³ + 3x² - 5x + 8

› p(x) ÷ (x + 1)

To find:

› Remainder using remainder theorem.

Solution:

Remainder theorem:

When a polynomial p(x) is divided by (x - a), the remainder of p(x) is p(a).

⇒ (x + 1) = 0

x = -1

∴, x³ + 3x² - 5x + 8

=> (-1)³ + 3(-1)² - 5(-1) + 8

=> -1 + 3(1) - 5(-1) + 8

=> -1 + 3 + 5 + 8

=> -1 + 16

∴ 15

∴ The remainder is 15.