Question

Rozkład wielomianów na czynniki!!

1.W(x)=-4x^3+2x-6x+3

2.W(x)=20x^3+12x^2-45x-27

3.W(x)=8x^3-36x^2+54x-27

4.W(x)=x^4+2x^3-x-2

5.w(x)=x^5-x^3-125x^2+125

6.W(x)=x^4-1

7.W(x)=x^4+4x^2-5

Daję naj!!bardzo pilnę!!prosze pomóżcie!!!

Answer 1

1. w(x)= -4x³+2x²-6x+3=-4x³-6x+2x²+3=-2x(2x²+3)+(2x²+3)=(2x²+3)(-2x+1)

2. W(x)= 20x³+12x²-45x-27=20x³-45x+12x²-27= 20x(x²-45/20)+12(x²-27/12)=    

              20x(x²-9/4)+12(x²-9/4)= (x²-9/4)(20x+12)

3. W(x)=8x³-36x²+54x-27= 4x²(2x-9)+27(2x-1)

4. W(x)=x⁴+2x³-x-2=x³(x+2)-(x+2)=(x+2)(x³-1)

5. W(x)=x⁵-x³-125x²+125= x³(x²-1)-125(x²-1)= (x²-1)(x³-125)=(x-1)(x+1)(x³-125)

6. W(x)= x⁴-1=(x²-1)(x²+1)=(x-1)(x+1)(x²+1)

7. W(x)=x⁴+4x²-5=x⁴-x²+5x²-5=x²(x²-1)+5(x²-1)= (x²-1)(x²+5)=(x-1)(x+1)(x²+5)