factorise x^2+x-(a+1)(a+2)
Home
/
factorise x^2+x-(a+1)(a+2)
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
To factorise :
x² + x - ( a + 1 )( a + 2 )
Solution -
x² + x - ( a + 1 )( a + 2 )
=> x² + [ ( a + 2 ) - ( a + 1 ) ] x - ( a + 1 )( a + 2 )
=> x² + (a + 2) x - (a - 1 )x - ( a + 1 )( a + 2 )
=> x [ x + a + 2 ] - ( a + 1 ) [ x + a + 2 ]
=> [ x + a + 2 ][ x - a - 1 ] .
This is the required answer.
__________________________________
Additional Information -
( a + b )² = a² + 2ab + b²
( a - b )² = a² - 2ab + b²
( a + b )( a - b ) = a² - b²
( a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ca
_________________________________
Question :-
[tex] {x}^{2} + x - (a + 1)(a + 2)[/tex]
Solution :-
[tex] {x}^{2} + x - (a + 1)(a + 2)[/tex]
[tex] {x}^{2} + {(a + 2)(a + 1)} \times x - (a + 1)(a + 2)[/tex]
[tex] {x}^{2} + (a + 2)x - (a - 1)x - (a + 1)(a + 2)[/tex]
[tex]x(x + a + 2) - (a - 1)(x + a + 2)[/tex]
[tex](x + a + 2)(x - a - 2)[/tex]
Extra information :-
[tex](a + b )^{2} = {a}^{2} + {b}^{2} + 2.a.b[/tex]
[tex](a - b) ^{2} = {a}^{2} + {b}^{2} - 2.a.b[/tex]
[tex] {a}^{2} - {b}^{2} = (a + b)(a - b)[/tex]