Question

x³ - 3x² - 9x - 5 ÷ (x+1)​

Answer 1

Answer

Given that X³ – 3x² – 9x – 5

= x³ + x² – 4x² – 4x – 5x – 5

= x²( x + 1) – 4x ( x + 1) – 5(x + 1)

= (x + 1)(x² – 4x – 5)

= (x + 1)(x² -5x + x – 5)

= (x + 1)(x – 5) (x + 1)

hence, (x +1), (x -5) and (x +1) are the factors of given polynomial .Given that X³ – 3x² – 9x – 5

= x³ + x² – 4x² – 4x – 5x – 5

= x²( x + 1) – 4x ( x + 1) – 5(x + 1)

= (x + 1)(x² – 4x – 5)

= (x + 1)(x² -5x + x – 5)

= (x + 1)(x – 5) (x + 1)

hence, (x +1), (x -5) and (x +1) are the factors of given polynomial .v

Answer 2

Answer:

Given :-

➪ x³ - 3x² - 9x - 5 ÷ (x + 1)

Solution :-

➪ x³ - 3x² - 9x - 5 ÷ (x + 1)

➭ x³ - 5x² + 2x² - 10x + x - 5/(x + 1)

➭ x²(x - 5) + 2x(x - 5) + 1(x - 5)/(x + 1)

➭ (x - 5) (x² + 2x + 1)/(x + 1)

➭ (x - 5) {x² + (1 + 1)x + 1}/(x + 1)

➭ (x - 5) {x² + x + x + 1}/(x + 1)

➭ (x - 5) {x(x + 1) + 1(x + 1)}/(x + 1)

➭ (x - 5) (x + 1) (x + 1)/(x + 1)

After cancellation, we get

➭ (x - 5) (x + 1)

∴ The value of x³ - 3x² - 9x - 5 ÷ (x + 1) is

(x - 5) (x + 1)