1.
5 * 3 + 1 = 15 + 1 = 16
(5 - 1)(5 + 2) = 4*7 = 28
2.
a)
[tex]A(x)=3x+1[/tex]
b)
[tex]A(x) = 0\\3x+1=0\\3x=-1\\x=-\frac{1}{3}[/tex]
3.
[tex]B(x)=(x-1)(x+2)\\= x^2+2x-x-2\\= x^2+x-2[/tex]
4.
[tex]B(x)-A(x) = (x-1)(x+2)-(3x+1)\\B(x)-A(x) = (x-1)(x+2)-3x-1\\B(x)-A(x) = x^2-2x-3\\\\(x+1)(x-3) = x^2-3x+x-3\\(x+1)(x-3) = x^2-2x-3\\\\Donc: \ B(x)-A(x) = (x+1)(x-3)[/tex]
5.
[tex]Rsoudre: A(x)=B(x)\\A(x)=B(x)\\3x+1=(x-1)(x+2)\\3x+1-(x^2+x-2)=0\\3x+1-x^2-x+2=0\\-x^2+2x+3=0\\x^2-2x-3=0\\(x-3)(x+1)=0\\\\x-3=0 \rightarrow x=3, \ \ \ \ \ x+1=0 \rightarrow x=-1\\\\S=\{3, -1\}\\[/tex]
On doit choisir 3 ou -1 pour que les deux programmes donnent le meme resultat. A(3) = 10, A(-1) = -2
