Question

Przedstaw w postaci iloczynu

a) a(b-3)+c(3-b) =
b) a²+a+ab+b=
c) a²+2a+1=
d) a²+3a+2=

Answer 1

Przedstaw w postaci iloczynu

a) a(b-3)+c(3-b) =
=a(b -3) - (b -3) =
= (b-3)( a -1)

b) a²+a+ab+b=
= a(a + 1) + b( a + 1) =
=(a + 1)( a + b)

c) a²+2a+1= ( a -a1)( a -a2)
= (a + 1)²

d) a²+3a+2=
Δ = 3² -4*1*2= 9 -8= 1
√Δ = √1 = 1
a1= (-3-1):2*1 = (-4) : 2 = (-2)
a2 = (-3 +1) :2*1 = (-2) : 2 = (-1)
a²+3a+2= ( a +2)(a +1)