Answer:
a = 2
b = 0
c = 3
Explanation:
if I understand correctly the problem should look like
2x⁴ + 2x³ + 5x² + 3x + 3 = (x² + x + 1)(ax² + bx + c)
let's calculate the right side
ax⁴ + ax³ + ax² + bx³ + bx² + bx + cx² + cx + c
as there is only one term of x⁴, we know a = 2
as there is only one term without any x, we know c = 3
now we get
2x⁴ + 2x³ + 2x² + bx³ + bx² + bx + 3x² + 3x + 3
remember, that is equal to
2x⁴ + 2x³ + 5x² + 3x + 3
after subtracting 2x⁴ and 3 from both sides we get
2x³ + 5x² + 3x = 2x³ + 2x² + bx³ + bx² + bx + 3x² + 3x
we subtract 2x³ and 3x from both sides and get
5x² = 2x² + bx³ + bx² + bx + 3x² = 5x² + bx³ + bx² + bx
we subtract 5x² from both sides and get
0 = bx³ + bx² + bx
=> b must be 0 to make this true for all values of x