Is x^2 = 144 rational or irrational

The roots are rational

Step-by-step explanation:

Given

x² = 144 ( take the square root of both sides )

x = ± = ± 12 ← both rational

A rational number can be expressed in the form

where a and b are integers.

12 = ← thus rational

- 12 = ← thus rational

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."