Question 351502
Please only submit ONE problem at a time.

1 {{{ (25b^3+15b^2+25b+38)/ (5b+5) }}}
I did long division on the problem, the reason i did the stars is so that you can see how everything lines up.


******5b^2-2b+7
5b+5**25b^3+15b^2+25b+38
****-(25b^3+25b^2)
***********-10b^2+25b+38
*********-(-10b^2-10b)
******************35b+38
****************-(35b+35)
***********************3 remainder
so the answer would  be 
{{{5b^2-2b+7+3/(5b+5)}}}
 

2. factor completely 4a^2+49-28a

{{{4a^2-28a+49 = (2a-7)(2a-7)}}}


3. solve, simplify your answer. type an exact answer using radicals as needed. Rationalize all denominators. Use a comma to separate answers. 
4x^4-8x^2+3=0
Let y = x² to make it easier.

{{{4y^2 - 8y + 3 = 0}}}
{{{(2y - 1)(2y - 3) = 0}}}
y = 1/2 or 3/2
x^2 = 1/2 or 3/2
{{{x = (+1)/(sqrt(2))}}} or {{{x=+(sqrt(3))/(sqrt(2))}}} or
{{{x = (-1)/(sqrt(2))}}} or {{{x=-(sqrt(3))/(sqrt(2))}}}
now we have to get rid of the radicals on the bottom, we do that by multiplying each answer by {{{ sqrt(2)/sqrt(2) }}}
{{{x = (sqrt(2)/2)}}} or {{{x=(sqrt(6))/2)}}} or
{{{x = -(sqrt(2)/2)}}} or {{{x=-(sqrt(6))/2)}}}






4. Multiply. (3x+4)(9x^2+3x+9)
{{{(3x+4)(9x^2+3x+9) = 27x^3+9x^2+27x+ 36x^2+12x+36 = 27x^3+45x^2+39x+36 }}}