Math friends, anyone help me?

Question

What is the result of 16x^4 + 32x^3 + 24x^2 + 8x + 1 divided by 2x + 1?

a. x^3 + 3x^2 + 3x + 1

b. 8x^3 + 12x^2 + 6x + 1

c. x^3 + 6x^2 + 4x

d. 4x^3 + 6x^2 + 4x + 1

Whose theorem is used to determine how many real zeroes are likely in this function, f(x) = 16x^4 – 3x^3 – 2x^2 + 8x?

a. Pascal’s

b. Einstein’s

c. Penrose’s

d. Descartes

Answer 1

For number 1 it should be b. since you are dividing by 2x + 1 and if you try to eliminate the first term of the part that you are dividing you would multiply with 8x^3 ...

# 2 i believe its d ..Descartes..but not a 100% sure

hope that helps :)