Wyznacz sumę W+Q...- Zadanie 2.4: Prosto do matury 2. Zakres podstawowy

Rozwiązanie

$a) W (x) + Q (x) = x^{3} - x^{2} + 6 x - 2 + 2 x^{3} - x^{2} + x + 4 = 3 x^{3} - 2 x^{2} + 7 x + 2$

$W (x) - Q (x) = x^{3} - x^{2} + 6 x - 2 - (2 x^{3} - x^{2} + x + 4) = x^{3} - x^{2} + 6 x - 2 - 2 x^{3} + x^{2} - x - 4 = - x^{3} + 5 x - 6$

$b) W (x) + Q (x) = 3 x^{3} - 5 x^{2} + 7 x - 1 - 4 x^{3} + 2 x^{2} - x + 5 = - x^{3} - 3 x^{2} + 6 x + 4$

$W (x) - Q (x) = 3 x^{3} - 5 x^{2} + 7 x - 1 - (- 4 x^{3} + 2 x^{2} - x + 5) = 3 x^{3} - 5 x^{2} + 7 x - 1 + 4 x^{3} - 2 x^{2} + x - 5 = 7 x^{3} - 7 x^{2} + 8 x - 6$

$c) W (x) + Q (x) = - 3 x^{4} + 2 x^{3} - x + 3 + x^{5} + 4 x^{3} + 2 x - 1 = x^{5} - 3 x^{4} + 6 x^{3} + x + 2$

$W (x) - Q (x) = - 3 x^{4} + 2 x^{3} - x + 3 - (x^{5} + 4 x^{3} + 2 x - 1) = - 3 x^{4} + 2 x^{3} - x + 3 - x^{5} - 4 x^{3} - 2 x + 1 = - x^{5} - 3 x^{4} - 2 x^{3} - 3 x + 4$

$d) W (x) + Q (x) = 4 x^{5} - 6 x^{3} + 11 + 4 x^{5} + 6 x^{3} + 3 = 8 x^{5} + 14$

$W (x) - Q (x) = 4 x^{5} - 6 x^{3} + 11 - (4 x^{5} + 6 x^{3} + 3) = 4 x^{5} - 6 x^{3} + 11 - 4 x^{5} - 6 x^{3} - 3 = - 12 x^{3} + 8$

$e) W (x) + Q (x) = 12 x^{4} - 3 x + 1 - 5 x^{4} + 3 x^{2} - 1 = 7 x^{4} + 3 x^{2} - 3 x$

$W (x) - Q (x) = 12 x^{4} - 3 x + 1 - (- 5 x^{4} + 3 x^{2} - 1) = 12 x^{4} - 3 x + 1 + 5 x^{4} - 3 x^{2} + 1 = 17 x^{4} - 3 x^{2} - 3 x + 2$

$f) W (x) + Q (x) = \frac{1}{2} x^{5} + \frac{3}{2} x^{2} - \frac{5}{2} x - \frac{3}{2} x^{3} - \frac{5}{2} x^{2} + \frac{1}{2} x - 1 = \frac{1}{2} x^{5} - \frac{3}{2} x^{3} - x^{2} - 2 x - 1$

$W (x) - Q (x) = \frac{1}{2} x^{5} + \frac{3}{2} x^{2} - \frac{5}{2} x - (- \frac{3}{2} x^{3} - \frac{5}{2} x^{2} + \frac{1}{2} x - 1) = \frac{1}{2} x^{5} + \frac{3}{2} x^{2} - \frac{5}{2} x + \frac{3}{2} x^{3} + \frac{5}{2} x^{2} - \frac{1}{2} x + 1 = \frac{1}{2} x^{5} + \frac{3}{2} x^{3} + 4 x^{2} - 3 x + 1$

$g) W (x) + Q (x) = 0, 3 x^{3} - 0, 7 x^{2} + 0, 1 x + 3, 1 - 2, 7 x^{3} + 1, 7 x^{2} - 0, 9 x + 2, 1 = - 2, 4 x^{3} + x^{2} - 0, 8 x + 5, 2$

$W (x) - Q (x) = 0, 3 x^{3} - 0, 7 x^{2} + 0, 1 x + 3, 1 - (- 2, 7 x^{3} + 1, 7 x^{2} - 0, 9 x + 2, 1) = 0, 3 x^{3} - 0, 7 x^{2} + 0, 1 x + 3, 1 + 2, 7 x^{3} - 1, 7 x^{2} + 0, 9 x - 2, 1 = 3 x^{3} - 2, 4 x^{2} + x + 1$

$h) W (x) + Q (x) = 3 x^{4} - 0, 2 x^{3} - x^{2} + 1, 1 x - 7 + 0, 8 x^{3} + 2 x^{2} - 3, 9 x + 1 = 3 x^{4} + 0, 6 x^{3} + x^{2} - 2, 8 x - 6$

$W (x) - Q (x) = 3 x^{4} - 0, 2 x^{3} - x^{2} + 1, 1 x - 7 - (0, 8 x^{3} + 2 x^{2} - 3, 9 x + 1) = 3 x^{4} - 0, 2 x^{3} - x^{2} + 1, 1 x - 7 - 0, 8 x^{3} - 2 x^{2} + 3, 9 x - 1 = 3 x^{4} - x^{3} - 3 x^{2} + 5 x - 8$

Aleksandra Filipowska

Nauczycielka matematyki

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