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Rozkład wielomianu na czynniki

Authored by Olga Dąbkowska

Mathematics

1st - 3rd Grade

Used 100+ times

Rozkład wielomianu na czynniki
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7 questions

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1.

MULTIPLE SELECT QUESTION

1 min • 1 pt

Rozłóż wielomian na czynniki

 w(x)=x7−x5w\left(x\right)=x^7-x^5  

 x5(x2−0)x^5\left(x^2-0\right)  

 x7(1−x2)x^7\left(1-x^2\right)  

 x5(x2−1)x^5\left(x^2-1\right)  

nie można rozłożyć tego wielomianu

2.

MULTIPLE SELECT QUESTION

1 min • 1 pt

Rozłóż wielomian na czynniki

 w(x)=x5−4x4+4x3w\left(x\right)=x^5-4x^4+4x^3  

 x3(x2−4)x^3\left(x^2-4\right)  

 x3(x2+4x−4)x^3\left(x^2+4x-4\right)  

 x3(x2−4x+4)x^3\left(x^2-4x+4\right)  

 4x(x4−x3+x2)4x\left(x^4-x^3+x^2\right)  

3.

MULTIPLE SELECT QUESTION

5 mins • 1 pt

Rozkładem na czynniki wielomianu

 w(x)=8x3−27w\left(x\right)=8x^3-27  jest: 

 (2x−3)(4x2−6x+9)\left(2x-3\right)\left(4x^2-6x+9\right)  

 (2x−3)(4x2−12x−9)\left(2x-3\right)\left(4x^2-12x-9\right)  

 (2x−3)(4x2−12x+9)\left(2x-3\right)\left(4x^2-12x+9\right)  

 (2x−3)(4x2+6x+9)\left(2x-3\right)\left(4x^2+6x+9\right)  

4.

MULTIPLE SELECT QUESTION

5 mins • 1 pt

Rozłóż wielomian na czynniki

 (2x2+x−1)(x2−3x+2)\left(2x^2+x-1\right)\left(x^2-3x+2\right)  

 2(x+1)2(x−12)(x−2)2\left(x+1\right)^2\left(x-\frac{1}{2}\right)\left(x-2\right)  

 2(x+1)(x−12)(x−1)(x−2)2\left(x+1\right)\left(x-\frac{1}{2}\right)\left(x-1\right)\left(x-2\right)  

 2(x+1)(x+12)(x−1)(x+2)2\left(x+1\right)\left(x+\frac{1}{2}\right)\left(x-1\right)\left(x+2\right)  

 2(x−1)(x+12)(x+1)(x+2)2\left(x-1\right)\left(x+\frac{1}{2}\right)\left(x+1\right)\left(x+2\right)  

5.

MULTIPLE SELECT QUESTION

3 mins • 1 pt

Rozłóż wielomian na czynniki z użyciem wzorów skróconego mnożenia

 w(x)=8x3−1w\left(x\right)=8x^3-1  

 (2x−1)(4x2−2x+1)\left(2x-1\right)\left(4x^2-2x+1\right)  

 (2x−1)(2x2+2x+1)\left(2x-1\right)\left(2x^2+2x+1\right)  

 (2x+1)(4x2+2x+1)\left(2x+1\right)\left(4x^2+2x+1\right)  

 (2x−1)(4x2+2x+1)\left(2x-1\right)\left(4x^2+2x+1\right)  

6.

MULTIPLE SELECT QUESTION

2 mins • 1 pt

Rozłóż wielomian na czynniki, grupując jego wyrazy

 w(x)=x3−2x2+x−2w\left(x\right)=x^3-2x^2+x-2  

 (x+1)2(x−2)\left(x+1\right)^2\left(x-2\right)  

 (x−1)(x+1)(x−2)\left(x-1\right)\left(x+1\right)\left(x-2\right)  

 (x2+1)(x+2)\left(x^2+1\right)\left(x+2\right)  

 (x2+1)(x−2)\left(x^2+1\right)\left(x-2\right)  

7.

MULTIPLE SELECT QUESTION

3 mins • 1 pt

Rozłóż wielomian na czynniki, grupując jego wyrazy:

 w(x)=x3−x2−3x+3w\left(x\right)=x^3-x^2-3x+3  

 (x−1)(x−3)(x+3)\left(x-1\right)\left(x-\sqrt{3}\right)\left(x+\sqrt{3}\right)  

 (x−1)(x2+3)\left(x-1\right)\left(x^2+3\right)  

 (x+1)(x−3)(x+3)\left(x+1\right)\left(x-\sqrt{3}\right)\left(x+\sqrt{3}\right)  

 (x+1)(x2+3)\left(x+1\right)\left(x^2+3\right)  

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