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}

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

3/4 ÷ 3/4

step-by-step explanation:

basically divide any proper fraction with itself to fit the criteria.

so if we are using 3/4, then:

3/4 ÷ 3/4 = 1

so 1 is the quotient.

and the numerators for both these fractions is 3.   and if we divide the numerators:

3 ÷ 3 = 1

we see that quotient is equal to our original quotient as well.

the 3rd on is correct

step-by-step explanation:

a

step-by-step explanation: