Question

a)x(puterea 3)+5x(puterea 2)+x+5
b)x(puterea 3)+x(puterea 2)+6x+6
c)x(puterea 3)-2x(puterea 2)+10x-20
d)4x(puterea 3)+4x(puterea 2)-9x-9
e)2x(puterea 3)-8x(puterea 2)-3x+12
f)x(puterea 4)+3x(puterea 3)+8x+24

Answer 1

a) x³+5x²+x+5= x²(x+5) + 1(x+5)= (x+5)* (x²+1)
b) x³+x²+6x+6= x²(x+1) +6(x+1)= (x+6)*(x²+1)
c) x³-2x²+10x-20 = x²(x-2) + 10(x-2)= (x-2) * (x²+10)
d) 4x³+4x²-9x-9= 4x²(x+1)-9(x+1)= (x+1) (4x²-9) = (x+1) * (2x-3) * (2x+3)
e) 2x³-8x²-3x+12= 2x² (x-4) - 3(x-4) = (x-4) * (2x²-3) = (x-4) * (√2x+√3) * (√2x-√3)
f) x⁴+3x³+8x+24= x³(x+3)+8(x+3)= (x+3) * (x³+8)= (x+3) * (x+2) *(x²-2x+4)