1.a) 2 (x-1)² -8
=2(x²-2x+1)-8
=2x² -4x +2-8
=2x² -4x -6
= p(x)
b) 2 (x-3) (x+1)
= 2(x²+x -3x -3)
=2x² + 2x -6x -6
=2x² -4x -6
= p(x)
2.a) * p(3) = 2 (3-1)² -8 = 2x2²-8 = 2³-8 =8-8=0
*p(1+√2) = 2 (1+√2-3) (1+√2+1) = 2(√2-2)(√2+2)=2(√2²+2√2-2√2-4)=2(2-4)=-4
b) p(x) =0
⇔2 (x-3) (x+1) =0
⇔ (x-3) =0 ou (x+1) =0
⇔ x=3 ou x=-1
*p(x)=-8
⇔2 (x-1)² -8 = -8
⇔2 (x-1)² =0
⇔ (x-1)²=0
⇔ x-1=0
⇔x=1
*p(x)=-6
⇔2x² -4x -6 =-6
⇔2x² -4x =0
⇔ x (2x-4) =0
⇔ x=0 ou 2x-4=0
⇔x=0 ou x=2
