Bonsoir²,
Help me por favor : )
Factoriser :
p(x) = (2x +1) (x-3) - (4x + 5)(3 - x) ; Q(x) = 2x² + 5x - 3 ;R(x)= (x² -4)² - (x + 2)² ;
S(x) = x³ - 2x² -5x +6 ; T(x) = x^4 +x³ -4x-16
Merci de m'aider : ).
Help me por favor : )
Factoriser :
p(x) = (2x +1) (x-3) - (4x + 5)(3 - x) ; Q(x) = 2x² + 5x - 3 ;R(x)= (x² -4)² - (x + 2)² ;
S(x) = x³ - 2x² -5x +6 ; T(x) = x^4 +x³ -4x-16
Merci de m'aider : ).
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Bonsoir,p(x)= (2x+1)(x-3) -(4x+5)(3-x)
=(2x+1)(x-3) + (4x+5)(-3+x) ( on changeant les signes de 3 et -x et on change le signe + qui est devant le terme (4x+5)(3-x)
donc p(x)= (2x+1)(x-3) +(4x+5)(x-3)
=(x-3)(2x+1 +4x+5)
= (x-3)(6x+6) = (x+3)*6(x+1)
donc p(x) =6(x-3)(x+1)
Q(x) = 2x² +5x -3 = 2x² +6x -x-3 = 2x(x+3) -(x+3)
Q(x) = (x+3) (2x+1) ( On peut faire Δ et on trouve comme racines -3 et 1/2 et on peut factoriser Q(x)= 2(x+3)(x-1/2))
R(x) = (x²-4)² -(x+2)² =[(x-2)(x+2)]² -(x+2)²
=[(x-2)(x+2) -(x+2)][(x-2)(x+2) +(x+2)]
=[(x+2)(x-2-1)][(x+2)(x-2 +1)]
=(x+2)(x-3)(x+2)(x-1)
=( x+2)²(x-3)(x-1)
S(x)= x³ -2x² -5x +6 = x³ -2x² +x -6x +6 ( car -x+6x=5x)
= x(x² -2x +1) -6(x-1)
=x(x-1)² -6(x-1)
=(x-1)[ x(x-1) -6]
= (x-1)(x²-x -6)
on doit factoriser x²-x-6; on calcule Δ et on trouve Δ=25 et deux racines 3 et -2
donc x²-x-6 =(x-3)(x+2)
donc S(x) = (x-1)(x-3)(x+2).
T(x) = x^4 +x³ -4x -16
=(x^4 -16) + ( x³-4x)
=( (x²)² -4²) + x( x²-4)
= (x²-4)(x²+4) +x(x²-4)
=( x²-4)(x²+4 +x)
= (x-2)(x+2)(x²+x+4).