Question

Rozłóz wielomian na w na czynniki.

a)w(x)=x3-2x2-x+2

b)w(x)=x3+3x2-4x-12

c)w(x)=3x3-x2+6x-2

d)w(x)=5x3-x2-10x+2

2.Rozłóz wielomian w na czynniki.

a)w(x)=(x+3)2-(2x+1)2

b)w(x)=(2x-4)2-(2-x)2

c)w(x)=5(x-1)5-20(x-1)4

d)w(x)=4(x+1)5-8(x+1)3

Answer 1

1

a.)   w(x)=x(x^2-1)2(x^2+1)

       w(x)=(2+x)(x^2-1)

b.)   w(x)=x(x^2-4)3(x^2-4)

       w(x)=(x+3)(x^2-4)

c.)   w(x)=x^2(3x-1)2(3x-1)

       w(x)=(x^2+2)(3x-1)

d.)   w(x)=x^2(5x-1)-2(5x-1)

       w(x)=(x^2-2)(5x-1)

2

a.)  w(x) = x^2+6x+9-4x^2-4x-1=-3x^2+2x+8= -3x^2+2(x+4)

b.)  w(x)=4x^2-16x+16-4+4x-x^2 = 3x^2-12x+12=3(x^2-6x+6)

c.)  w(x)=5(x^5-1)-20(x^4+1)=5x^5-5-20x^4-20=5x^5-20x^4-25=5(x^5-4x^4-5)

d.)  w(x)=4(x^5+1)-8(x^3+1)=4x^5+4-8x^3-8=4(x^5-2x^3-1)