Question

DESCOMPUNE IN FACTORI. rezolvare completa.

Answer 1

23. a) x²-9x+20 = x²-4x-5x+20 = x(x-4)-5(x-4) = (x-5)(x-4)
b) x²-8x+12 = x²-2x-6x+12 = x(x-2)-6(x-2) = (x-6)(x-2)

24. a) x²-4x-5 = x²+x-5x-5 = x(x+1)-5(x+1) = (x-5)(x+1)
b) x²+2x-8 = x²+4x-2x-8 = x(x+4)-2(x+4) = (x-2)(x+4)

25. a) 2x²+5x-3 = 2x²+6x-x-3 = 2x(x+3)-(x+3) = (2x-1)(x+3)
b) 5x²+3x-2  = 5x²+5x-2x-2 = 5x(x+1)-2(x+1) = (5x-2)(x+1)

26. a) x²+x-2x-x = x(x+1)-2(x+1) = (x-2)(x+1)
b) x³-x²-4x+4 = x²(x-1)-4(x-1) = (x²-4)(x-1) = (x-2)(x+2)(x-1)

Answer 2

23.
a) x²-9x+20=x²-2×9/2×x +(9/2)²-(9/2)²+20=(x-9/2)²-81/4+20=
=(x-9/2)²-81/4+80/4=(x-9/2)²-1/4=(x-9/2-1/2)(x-9/2+1/2)=(x-5)(x-4)

b) x²-8x+12=x²-8x+16-4=(x-4)²-2²=(x-4+2)(x-4-2)=(x-2)(x-6)


24.
a) x²-4x-5=x²-4x+4-9=(x-2)²-3²=(x-2+3)(x-2-3)=(x+1)(x-5)

b) x²+2x-8=x²+2x+1-9=(x+1)²-3²=(x+1+3)(x+1-3)=(x+4)(x-2)


25.
a) 2x²+5x-3=2(x²+5x/2-3/2)=2(x²+2×5x/4+(5/4)²-(5/4)²-3/2)=
=2[(x+5/4)²-25/16-24/16]=2[(x+5/4)²-49/16]=2(x+5/4-7/4)(x+5/4+7/4)=
=2(x-2/4)(x+3)=(2x-1)(x+3)

b) 5x²+3x-2=5(x²+3x/5-2/5)=5[x²+2×3x/10+(3/10)²-(3/10)²-2/5]=
=5[(x+3/10)²-9/100-40/100]=5[(x+3/10)²-49/100]=
=5(x+3/10-7/10)(x+3/10+7/10)=5(x-4/10)(x+1)=5(x-2/5)(x+1)=(5x-2)(x+1)

26
a)x²+x-2x-2=x(x+1)-2(x+1)=(x+1)(x-2)

b)x³-x²-4x+4=x²(x-1)-4(x-1)=(x-1)(x²-4)=(x-1)(x-2)(x+2)