Which of the following are subspaces of p3? support your answer.
a. u = { f(x) | f(x) ∈ p3, f(2) = 1}
b. u = {xg(x) | g(x) ∈ p2}
c. u = {xg(x) | g(x) ∈ p3}
d. u = {xg(x) + (1−x)h(x) | g(x) and h(x) ∈ p2}
e. u = the set of all polynomials in p3 with constant term 0
f. u = { f(x) | f(x) ∈ p3, deg f(x) = 3}

[2, 2.5)

(2.5, 3]

step-by-step explanation:

i think its these two not sure [2, 2.5)

(2.5, 3]

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)

the answer for your question is

step-by-step explanation: