Question

Rozłóż na czynniki:

1. a) 10x^(3)+25x^(2)-8x+20

b) 3(x-1)(x+2)-2x(x-1)(x+3)

c) -24x^(4)-120x^(3)-150x

d) 5x^(5)+2x^(4)+10x^(3)+4x^(2)

Answer 1

a) 10x³+25x²-8x+20=5x²(2x+5)-4(2x+5)=(√5x-2)(√5x+2)(2x+5)

b) 3(x-1)(x+2)-2x(x-1)(x+3)=(x-1)[3(x+2)-2x(x+3)]

c)-24x⁴-120x³+30x²-150x=24x⁴+120x³-30x²+150x=24x³(x+5)+30x(x+5)=6x(4x²+5)(x+5)

d) 5x⁵+2x⁴+10x³+4x²=x³(5x²+2x)+2x(5x²+2x)=(x³+2x)(5x²+2x)=x²(x²+2)(5x+2)