Dane są wielomiany:
W(x)= x²+x+1
P(x)=2x³ -7x+3
Q(x)=-3x³+4x²-9x+1
Wykonaj działania:
1. [W(x)] ²
2. P(x)*Q(x)
3.W(x)*(P(x)+4Q(x))
4. W(x)*(P(x)-Q(x))
wyniki:
1.x^4+2x^3+3x^2+2x+1
2.-6x^6+8x^5+3x^4-35x^3+75x^2-34x+3
3.-10x^5+6x64-37x^3-20x^2-36x+7
4.5x^5+x^4+3x^3+4x+2
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1. [W(x)] ²
2. P(x)*Q(x)
2.![P(x)Q(x)=(2x^{3} -7x+3)(-3x^{3}+4x^{2}-9x+1)=\\ -6x^{6}+8x^{5}-18x^{4}+2x^{3}+21x^{4}-28x^{3}+63x^{2}-7x-\\ -9x^{3}+12x^{2}-27x+3=\\ -6x^{6}+8x^{5}+3x^{4}-35x^{3}+75x^{2}-34x+3 P(x)Q(x)=(2x^{3} -7x+3)(-3x^{3}+4x^{2}-9x+1)=\\ -6x^{6}+8x^{5}-18x^{4}+2x^{3}+21x^{4}-28x^{3}+63x^{2}-7x-\\ -9x^{3}+12x^{2}-27x+3=\\ -6x^{6}+8x^{5}+3x^{4}-35x^{3}+75x^{2}-34x+3](https://tex.z-dn.net/?f=P%28x%29Q%28x%29%3D%282x%5E%7B3%7D+-7x%2B3%29%28-3x%5E%7B3%7D%2B4x%5E%7B2%7D-9x%2B1%29%3D%5C%5C+-6x%5E%7B6%7D%2B8x%5E%7B5%7D-18x%5E%7B4%7D%2B2x%5E%7B3%7D%2B21x%5E%7B4%7D-28x%5E%7B3%7D%2B63x%5E%7B2%7D-7x-%5C%5C+-9x%5E%7B3%7D%2B12x%5E%7B2%7D-27x%2B3%3D%5C%5C+-6x%5E%7B6%7D%2B8x%5E%7B5%7D%2B3x%5E%7B4%7D-35x%5E%7B3%7D%2B75x%5E%7B2%7D-34x%2B3+)
3. W(x)*(P(x)+4Q(x))
(P(x)+4Q(x))=(2x³ -7x+3)+(-12x^{3}+16x^{2}-36x+4)
W(x)*(P(x)+4Q(x)) = (x²+x+1)(-10x^{3}+16x^{2}-43x+7)=
=![(x^{2}+x+1)(-10x^{3}+16x^{2}-43x+7)=\\ =-10x^{5}+16x^{4}-43x^{3}+7x^{2}-10x^{4}+16x^{3}-43x^{2}+7x-\\ -10x^{3}+16x^{2}-43x+7=-10x^{5}+6x^{4}-53x^{3}+6x^{2}-36x+7 (x^{2}+x+1)(-10x^{3}+16x^{2}-43x+7)=\\ =-10x^{5}+16x^{4}-43x^{3}+7x^{2}-10x^{4}+16x^{3}-43x^{2}+7x-\\ -10x^{3}+16x^{2}-43x+7=-10x^{5}+6x^{4}-53x^{3}+6x^{2}-36x+7](https://tex.z-dn.net/?f=%28x%5E%7B2%7D%2Bx%2B1%29%28-10x%5E%7B3%7D%2B16x%5E%7B2%7D-43x%2B7%29%3D%5C%5C+%3D-10x%5E%7B5%7D%2B16x%5E%7B4%7D-43x%5E%7B3%7D%2B7x%5E%7B2%7D-10x%5E%7B4%7D%2B16x%5E%7B3%7D-43x%5E%7B2%7D%2B7x-%5C%5C+-10x%5E%7B3%7D%2B16x%5E%7B2%7D-43x%2B7%3D-10x%5E%7B5%7D%2B6x%5E%7B4%7D-53x%5E%7B3%7D%2B6x%5E%7B2%7D-36x%2B7)
4. W(x)*(P(x)-Q(x))
(P(x)-Q(x))=(2x³ -7x+3)-(-3x³+4x²-9x+1)=
=![(2x^{3} -7x+3)-(-3x^{3}+4x^{2}-9x+1)=2x^{3} -7x+3+3x^{3}-4x^{2}+9x-1=\\ =5x^{3}-4x^{2}+2x+2 (2x^{3} -7x+3)-(-3x^{3}+4x^{2}-9x+1)=2x^{3} -7x+3+3x^{3}-4x^{2}+9x-1=\\ =5x^{3}-4x^{2}+2x+2](https://tex.z-dn.net/?f=%282x%5E%7B3%7D+-7x%2B3%29-%28-3x%5E%7B3%7D%2B4x%5E%7B2%7D-9x%2B1%29%3D2x%5E%7B3%7D+-7x%2B3%2B3x%5E%7B3%7D-4x%5E%7B2%7D%2B9x-1%3D%5C%5C+%3D5x%5E%7B3%7D-4x%5E%7B2%7D%2B2x%2B2)
W(x)*(P(x)-Q(x)) = (x²+x+1)(5x^{3}-4x^{2}+2x+2)=
=![(x^{2}+x+1)(5x^{3}-4x^{2}+2x+2)=5x^{5}-4x^{4}+2x^{3}+2x^{2}+\\ =5x^{4}-4x^{3}+2x^{2}+2x+5x^{3}-4x^{2}+2x+2=\\ =5x^{4}+x^{3}-2x^{2}+4x+2 (x^{2}+x+1)(5x^{3}-4x^{2}+2x+2)=5x^{5}-4x^{4}+2x^{3}+2x^{2}+\\ =5x^{4}-4x^{3}+2x^{2}+2x+5x^{3}-4x^{2}+2x+2=\\ =5x^{4}+x^{3}-2x^{2}+4x+2](https://tex.z-dn.net/?f=%28x%5E%7B2%7D%2Bx%2B1%29%285x%5E%7B3%7D-4x%5E%7B2%7D%2B2x%2B2%29%3D5x%5E%7B5%7D-4x%5E%7B4%7D%2B2x%5E%7B3%7D%2B2x%5E%7B2%7D%2B%5C%5C+%3D5x%5E%7B4%7D-4x%5E%7B3%7D%2B2x%5E%7B2%7D%2B2x%2B5x%5E%7B3%7D-4x%5E%7B2%7D%2B2x%2B2%3D%5C%5C+%3D5x%5E%7B4%7D%2Bx%5E%7B3%7D-2x%5E%7B2%7D%2B4x%2B2)