Question

Divide : 1) (x²-2x-24) ÷ (x-6)​

Answer 1

Given:

(x² - 2x - 24) ÷ (x - 6)​

What To Do:

We have to divide the given expression.

Solution:

(x² - 2x - 24) ÷ (x - 6)​

Also written as,

$\sf \Rightarrow \dfrac{ (x^2 - 2x - 24) }{ (x - 6) }$

By using the splitting the middle term,

⇒ i.e -2x = -6x + 4x and -24 = -6 × 4

By using the identity i.e (x + a) (x + b) = x² + x(a + b) + ab

⇒ Where x² = x², a = -6 and b = 4

Coming to the expression,

$\sf \Rightarrow \dfrac{(x^2 - 6x) + (4x - 24)} {(x - 6)}$

Take out the common factors in x² - 6x i.e x,

$\sf \Rightarrow \dfrac{ x(x - 6) + (4x - 24)} {(x - 6)}$

Take out the common factors in 4x - 24 i.e 4,

$\sf \Rightarrow \dfrac{ x(x - 6) + 4(x - 6)} {(x - 6)}$

Add x and 4 and take x - 6 as common,

$\sf \Rightarrow \dfrac{ (x - 6) (x + 4) } {(x - 6)}$

Cancel x - 6 in numerator and denominator,

⇒ x + 4

∴ Thus, the answer is x + 4.

Answer 2

Given:

(x² - 2x - 24) ÷ (x - 6)

What To Do:

We have to divide the given expression.

Solution:

(x² - 2x - 24) ÷ (x - 6)

Also written as,

$\sf \Rightarrow \dfrac{ (x^2 - 2x - 24) }{ (x - 6) }$

By using the splitting the middle term,

⇒ i.e -2x = -6x + 4x and -24 = -6 × 4

By using the identity i.e (x + a) (x + b) = x² + x(a + b) + ab

⇒ Where x² = x², a = -6 and b = 4

Coming to the expression,

$\sf \Rightarrow \dfrac{(x^2 - 6x) + (4x - 24)} {(x - 6)}$

Take out the common factors in x² - 6x i.e x,

$\sf \Rightarrow \dfrac{ x(x - 6) + (4x - 24)} {(x - 6)}$

Take out the common factors in 4x - 24 i.e 4,

$\sf \Rightarrow \dfrac{ x(x - 6) + 4(x - 6)} {(x - 6)}$

Add x and 4 and take x - 6 as common,

$\sf \Rightarrow \dfrac{ (x - 6) (x + 4) } {(x - 6)}$

Cancel x - 6 in numerator and denominator,

⇒ x + 4

∴ Thus, the answer is x + 4.