Rozłóż na czynniki wielomiany ...- Zadanie 5.48.: Matematyka 2. Poziom podstawowy. Po gimnazjum

Rozwiązanie

$a)$

$W (x) = x^{3} + 3 x^{2} - 4 x - 12 = x^{2} (x + 3) - 4 (x + 3) = (x + 3) (x^{2} - 4) = (x + 3) (x - 2) (x + 2)$

$b)$

$W (x) = 7 x^{3} + 2 x^{2} - 21 x - 6 = x^{2} (7 x + 2) - 3 (7 x + 2) = (7 x + 2) (x^{2} - 3) = (7 x + 2) (x - 3) (x + 3)$ $W (x) = 7 x^{3} + 2 x^{2} - 21 x - 6 = x^{2} (7 x + 2) - 3 (7 x + 2) = (7 x + 2) (x^{2} - 3) = (7 x + 2) (x - 3) (x + 3)$

$c)$

$W (x) = 9 x^{3} - 4 x^{2} - 27 x + 12 = x^{2} (9 x - 4) - 3 (9 x - 4) = (9 x - 4) (x^{2} - 3) = (9 x - 4) (x - 3) (x + 33)$

$d)$

$W (x) = x^{3} - x^{2} + x - 1 = x^{2} (x - 1) + (x - 1) = (x - 1) (x^{2} + 1)$

$e)$

$W (x) = 4 x^{3} + 4 x^{2} - x - 1 = 4 x^{2} (x + 1) - (x + 1) = (x + 1) (4 x^{2} - 1) = (x + 1) (2 x - 1) (2 x + 1)$

$f)$

$W (x) = - 9 x^{3} - 18 x^{2} + x + 2 = - 9 x^{2} (x + 2) + (x + 2) = (x + 2) (1 - 9 x^{2}) = (x + 2) (1 - 3 x) (1 + 3 x)$

$g)$

$W (x) = - 3 x^{3} - 4 x^{2} + 12 x + 16 = - x^{2} (3 x + 4) + 4 (3 x + 4) = (3 x + 4) (4 - x^{2}) = (3 x + 4) (2 - x) (2 + x)$

$h)$

$W (x) = 20 x^{3} + 12 x^{2} - 45 x - 27 = 5 x (4 x^{2} - 9) + 3 (4 x^{2} - 9) = (4 x^{2} - 9) (5 x + 3) = (5 x + 3) (2 x - 3) (2 x + 3)$

Krystian

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