Question

Rozłóż na czynniki (wielomiany)

zad w załączniku.

Answer 1

a)

 

x⁴ - x² -12 = 0

x⁴ - x² -16 + 4 = 0

x⁴ - 16 - x² + 4 = 0

(x² - 4)(x² + 4) - (x² - 4) = 0

(x² - 4)[(x² + 4) - 1] = 0

(x² - 4)[x² + 3] = 0

(x - 2)(x + 2)[x² + 3] = 0

 

b)

 

x⁴ - 3x² - 10= 0

x⁴ - 4 -3x² - 6 = 0

(x²-2)(x²+2)-3(x²+2)= 0

(x²+2)(x² - 2 - 3) = 0

(x²+2)(x² - 5) = 0

(x²+2)(x - √5)(x + √5) =0

 

c)

 

x⁴ - 11x² + 18 = 0

x⁴ - 4 - 11x² + 22 = 0

(x² -2)(x² +2) -11(x² - 2) = 0

(x² -2)(x² + 2 - 11) = 0

(x² -2)(x² - 9) = 0

(x - √2)(x + √2)(x - 3)(x + 3) = 0

 

d)

 

x⁴ + 10x² + 21 = 0

x²(x² +3) + 7(x² +3) = 0

(x² +3)(x² + 7) = 0

 

e)

 

4x⁴ +19x² - 5 = 0

4x⁴ - x² + 20x² - 5 = 0

x²(4x² - 1) +5(4x² - 1) = 0

(4x² - 1)(x² + 5) = 0

4(x² - 1/4)(x² + 5) = 0

4(x - 1/2)(x + 1/2)(x² + 5) = 0

 

f)

 

-9x⁴ - 8x² + 1 = 0

-(9x⁴ + 8x² - 1) = 0

-(9x⁴ -x² + 9x² - 1) = 0

-[x²(9x² - 1) + 9x² - 1] = 0

-(9x² - 1)(x² +1) = 0

-9(x² - 1/9)(x² + 1) = 0

-9(x- 1/3)(x + 1/3)(x² + 1) = 0

 

g)

 

x⁴ - 8x² + 16 = 0

x⁴ - 4x² - 4x² + 16 = 0

x²(x² - 4) - 4(x² - 4) = 0

(x² - 4)(x² - 4) = 0

(x² - 4)² = 0

((x - 2)(x + 2))² = 0

 

h)

 

81x⁴ - 18x² + 1 = 0

81x⁴ - 9x² - 9x² + 1 = 0

9x²(9x² - 1) - (9x² -1) = 0

(9x² - 1)(9x² - 1) = 0

(9x² - 1)² = 0

(9(x² - 1/9))² = 0

(9(x - 1/3)(x + 1/3))² = 0

81[(x - 1/3)(x + 1/3)]² = 0

Answer 2