Question

Factorise X + X - 24
Factorise x2 + 14x-51

Answer 1

1. 2(x - 12)

2. 16x - 51

Answer 2

➊ Factorise :- x + x - 24

Solution :-

`\longrightarrow\:\:\sf\red{x+x-24}`

• Collect like terms

`\longrightarrow\:\:\sf\orange{2x-24}`

• Factor out 2 from the expression

`\longrightarrow\:\:\bf\pink{2(x-12)}`

____________________________

➋ Factorise :- x² + 14x - 15

Solution :-

`\longrightarrow\:\:\sf\red{x^(2)+14x-15}`

• Rewrite -14x as a difference

`\longrightarrow\:\:\sf\orange{x^(2)+x-15x-15}`

• Factor out x from the expression

`\longrightarrow\:\:\sf\green{x * (x+1)-15x-15}`

• Factor out -15 from the expression

`\longrightarrow\:\:\sf\blue{x * (x+1)-15(x+1)}`

• Factor out x+1 from the expression

`\longrightarrow\:\:\bf\pink{(x+1)* (x-15)}\\`

(Refer the attachment for graph)

Graph Details :-

`\bigstar\:\:\bf{y = x^(2)-14x-15}`

• 
  `\rm{Roots\:\:(-1,\:0)\:(15,\:0)}`

• 
  `\rm{Domain\:\: x \in {\mathbb{R}}}`

• 
  `\rm{Range\:\:y \in (-64,\:+\infty)}`

• 
  `\rm{Minimum\:\:(7,\:-64)}`

• 
  `\rm{Vertical \:intercept\:\:(0,\:-15)}`