Bonjour,
Exercice 9 :
[tex]A(x)= \frac{(x-1)^2}{2^2}+ \frac{x(x+4)}{3}= \frac{(x-1)^2}{4}+ \frac{x(x+4)}{3}= \frac{3(x-1)^2}{3*4}+ \frac{4x(x+4)}{4*3} =[/tex] [tex]\frac{3(x^2-2x+1)}{12}+ \frac{4x^2+16x}{12} = \frac{3x^2-6x+3}{12}+ \frac{4x^2+16x}{12} = \frac{3x^2-6x+3+4x^2+16x}{12} =[/tex] [tex]\frac{7x^2+10x+3}{12}[/tex]
[tex]B(x)= ( \frac{2x-1}{3})( \frac{2x+1}{3}) -1=\frac{(2x-1)(2x+1)}{3*3}-1= \frac{4x^2-1}{9}= \frac{4x^2-1}{9}-1[/tex] [tex]= \frac{4x^2-1}{9}- \frac{9}{9} = \frac{4x^2-1-9}{9} = \frac{4x^2-8}{9}[/tex]
Exercice 13 :
A(x) = (x+2)²-4(x+3)(x+2) = (x+2)((x+2)-4(x+3)) = (x+2)(x+2-4x-3) = (x+2)(-3x-1)
B(x) = (x+5)(x-5)-9(2x+1)(10x-50) = (x+5)(x-5)-9(2x+1)(x-5)10 = (x+5)(x-5)-90(2x+1)(x-5) = (x-5)((x+5)-90(2x+1)) = (x-5)(x+5-180x-90) = (x-5)(-179x-85)
