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FACTORISER AVEC UN FACTEUR COMMUN
Factoriser une expression, c'est la transformer en un produit de facteurs. k a + a + b k b = k ( ) Fabienne BUSSAC k a – b a – k b = k ( ) Exemples : 4x + 12 = 4 x + x + 4 × 3 3 = 4 ( ) 7x² – 9x = 7x 7x × x – 9 – 9 × x = x ( )
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Fabienne BUSSAC [ ] [ ] [ ] [ ] A = (2x + 1)(7x – 3) + (2x + 1)(x + 2)
On repère le facteur commun A = (2x + 1) (2x + 1) (7x – 3) + (7x – 3) + (2x + 1) (2x + 1) (x + 2) (x + 2) [ ] A = (2x + 1) [ ] A = (2x + 1) 7x – 3 + x + 2 A = (2x + 1) ( 8x – 1 ) Fabienne BUSSAC B = (5x – 4)(6x – 1) – (5x – 4)(4x + 4) B = (5x – 4) (6x – 1) – (6x – 1) – (5x – 4) (4x + 4) (4x + 4) [ ] B = (5x – 4) [ ] B = (5x – 4) 6x – 1 – 4x – 4 B = (5x – 4) ( 2x – 5 )
![Fabienne BUSSAC [ ] [ ] [ ] [ ] A = (2x + 1)(7x – 3) + (2x + 1)(x + 2)](http://slideplayer.fr/slide/8463258/25/images/2/Fabienne+BUSSAC+%5B+%5D+%5B+%5D+%5B+%5D+%5B+%5D+A+%3D+%282x+%2B+1%29%287x+%E2%80%93+3%29+%2B+%282x+%2B+1%29%28x+%2B+2%29.jpg "On repère le facteur commun. A = (2x + 1) (2x + 1) (7x – 3) + (7x – 3) + (2x + 1) (2x + 1) (x + 2) (x + 2) [ ] A = (2x + 1) [ ] A = (2x + 1) 7x – 3 + x + 2. A = (2x + 1) ( 8x – 1. ) Fabienne BUSSAC. B = (5x – 4)(6x – 1) – (5x – 4)(4x + 4) B = (5x – 4) (6x – 1) – (6x – 1) – (5x – 4) (4x + 4) (4x + 4) [ ] B = (5x – 4) [ ] B = (5x – 4) 6x – 1 – 4x – 4. B = (5x – 4) ( 2x – 5. )")
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Fabienne BUSSAC [ ] [ ] C = (4x – 3)² – (x – 8)(4x – 3) C = (4x – 3)
![Fabienne BUSSAC [ ] [ ] C = (4x – 3)² – (x – 8)(4x – 3) C = (4x – 3)](http://slideplayer.fr/slide/8463258/25/images/3/Fabienne+BUSSAC+%5B+%5D+%5B+%5D+C+%3D+%284x+%E2%80%93+3%29%C2%B2+%E2%80%93+%28x+%E2%80%93+8%29%284x+%E2%80%93+3%29+C+%3D+%284x+%E2%80%93+3%29.jpg "Fabienne BUSSAC [ ] [ ] C = (4x – 3)² – (x – 8)(4x – 3) C = (4x – 3)")
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