Rozloz wielomian na czynniki
Ela: a) 12x2 + 14xy + 49y2 − 36x2
b) 25m2 − 4n2 −4n −1
c) b4 − 11b2 +10
13 lis 17:25
Robert nick: c) b
4 − 11b
2 +10
b
2 = t ⇒ t
2 − 11t + 10
Δ = (−11)
2 − 4*1*10 = 121 − 40 = 81,
√Δ = 9
| | 11 − 9 | | 11 + 9 | |
t1 = |
| = 1, t2 = |
| = 10 |
| | 2 | | 2 | |
t
2 − 11t + 10 = (t−1)(t−10)
t = b
2
⇒ b
4 − 11b
2 +10 = (b
2 − 1)(b
2 − 10) = (b − 1)(b + 1)(b −
√10)(b +
√10)
13 lis 17:56
Eta:
a) x2+14xy+49y2 −25x2= (x+7y)2−(5x)2= (x+7y+5x)(x+7y−5x)= (6x+7y)(7y−4x)
b) (5m)2 −(2n+1)2= (5m+2n+1)(5m−2n−1)
c) b4−b2−10b2+10= b2(b2−1)−10(b2−1)= (b2−1)(b2−10)= (b−1)(b+1)(b−√10)(b+√10)
13 lis 18:02