Dados los siguientes polinomios,

a) P(x) = 2x2 + 3x – 5 Q(x)= 2x + 4 S(x)= x –2. T(x)= 6x3 + 5x4 + 3x
b) U(x)= x2 – 2x + 4 W(x)= x5 – 3 V(x)= 3 + x2 – 2x3 + 5x
Realizar las siguientes operaciones:

1. 2U(x).S(x) + 4V(x)
2. S(x)3 + Q(x)2
3. [3P(x) + V(x)] : Q(x)2
4. W(x) . U(x) : P(x)
5. 3U(x) + S(x)2 – 2P(x).Q(x)
6. W(-1)
7. T(2)

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)