➊ Factorise :- x + x - 24
Solution :-
[tex]\longrightarrow\:\:\sf\red{x+x-24}[/tex]
[tex]\longrightarrow\:\:\sf\orange{2x-24}[/tex]
- Factor out 2 from the expression
[tex]\longrightarrow\:\:\bf\pink{2(x-12)}[/tex]
____________________________
➋ Factorise :- x² + 14x - 15
Solution :-
[tex]\longrightarrow\:\:\sf\red{x^{2}+14x-15}[/tex]
- Rewrite -14x as a difference
[tex]\longrightarrow\:\:\sf\orange{x^{2}+x-15x-15}[/tex]
- Factor out x from the expression
[tex]\longrightarrow\:\:\sf\green{x \times (x+1)-15x-15}[/tex]
- Factor out -15 from the expression
[tex]\longrightarrow\:\:\sf\blue{x \times (x+1)-15(x+1)}[/tex]
- Factor out x+1 from the expression
[tex]\longrightarrow\:\:\bf\pink{(x+1)\times (x-15)}\\[/tex]
(Refer the attachment for graph)
Graph Details :-
[tex]\bigstar\:\:\bf{y = x^{2}-14x-15}[/tex]
- [tex]\rm{Roots\:\:(-1,\:0)\:(15,\:0)}[/tex]
- [tex]\rm{Domain\:\: x \in {\mathbb{R}}}[/tex]
- [tex]\rm{Range\:\:y \in (-64,\:+\infty)}[/tex]
- [tex]\rm{Minimum\:\:(7,\:-64)}[/tex]
- [tex]\rm{Vertical \:intercept\:\:(0,\:-15)}[/tex]
