Réponse :
Explications étape par étape
Bonjour
Factoriser :
60)
[tex]7x^{2} - 14x[/tex]
= 7x * x - 7x * 2
= 7x(x - 2)
[tex]16x^{2} - 81[/tex]
[tex]= (4x)^{2} - 9^{2}[/tex]
= (4x - 9)(4x + 9)
[tex]2a^{2}b - b[/tex]
[tex]= b * 2a^{2} - 1 * b[/tex]
[tex]= b(2a^{2} - 1)[/tex]
[tex]4x^{2} - 4x + 1[/tex]
[tex]= (2x)^{2} - 2 * 2x * 1 + 1^{2}[/tex]
[tex]= (2x - 1)^{2}[/tex]
61)
[tex]2(x - 1)^{2} + 3x - 3[/tex]
[tex]= 2(x - 1)^{2} + 3(x - 1)[/tex]
= (x - 1)[2(x - 1) + 3][/tex]
= (x - 1)(2x - 2 + 3)
= (x - 1)(2x + 1)
[tex]2x^{2} + 8x + 8[/tex]
[tex]= 2(x^{2} + 4x + 4)[/tex]
[tex]= 2(x + 2)^{2}[/tex]
[tex]x^{2} - 16 + (x - 4)^{2}[/tex]
[tex]= (x - 4)(x + 4) + (x - 4)^{2}[/tex]
= (x - 4)(x + 4 + x - 4)
= (x - 4)(2x)
= 2x(x - 4)
[tex]5x^{2} - 125[/tex]
[tex]= 5(x^{2} - 25)[/tex]
= 5(x - 5)(x + 5)
62)
[tex]x^{2} - 4 + (x - 2)(x + 1)[/tex]
= (x - 2)(x + 2) + (x - 2)(x + 1)
= (x - 2)(x + 2 + x + 1)
= (x - 2)(2x + 3)
[tex]3x^{2} - 12x + 12[/tex]
[tex]= 3(x^{2} - 4x + 4)[/tex]
[tex]= 3(x - 2)^{2}[/tex]
[tex]x^{2} + 3x + (x + 3)^{2}[/tex]
[tex]= x(x + 3) + (x + 3)^{2}[/tex]
= (x + 3)(x + x + 3)
= (x + 3)(2x + 3)
(x + 1)(x + 2) - (3x + 6)
= (x + 1)(x + 2) - 3(x + 2)
= (x + 2)(x + 1 - 3)
= (x + 2)(x - 2)
