Question

Descompuneti in factori ireductibili: a). x³-11x²+30x
b). x³-14x²+48x
c). x²(x²-10)+9
d). x²(x²-13)+36
e). (x²-x)(x²-x+7) -18
f). (x²+2x)(x²+2x-4)-5

Answer 1

f). (x²+2x)(x²+2x-4)-5a)x³-11x²+30x=x(x−5)(x−6)
b)x³-14x²+48x=x(x−6)(x−8)
c)x²(x²-10)+9=(x²)(x²)+(x²)(−10)+9=x4+−10x²+9
d)x²(x²-13)+36=(x2)(x2)+(x2)(−13)+36=x4+−13x2+36
e)(x²-x)(x²-x+7) -18=(x2)(x2)+(x2)(−x)+(x2)(7)+(−x)(x2)+(−x)(−x)+(−x)(7)+−18=x4+−x3+7x2+−x3+x2+−7x+−18=(x4)+(−x3+−x3)+(7x2+x2)+(−7x)+(−18)=x4+−2x3+8x2+−7x+−18
f). (x²+2x)(x²+2x-4)-5=(x2)(x2)+(x2)(2x)+(x2)(−4)+(2x)(x2)+(2x)(2x)+(2x)(−4)+−5=x4+2x3+−4x2+2x3+4x2+−8x+−5=(x4)+(2x3+2x3)+(−4x2+4x2)+(−8x)+(−5)=x4+4x3+−8x+−5