9514 1404 393
Answer:
4x^2 +16x +42 +92/(x -2)
Step-by-step explanation:
Synthetic division tells you the quotient is 4x^2 +16x +42 with a remainder of 92. To check this, we can multiply the quotient by the divisor and add the remainder:
(x -2)(4x^2 +16x +42) +92
= x(4x^2 +16x +42) -2(4x^2 +16x +42) +92
= 4x^3 +16x^2 +42x -8x^2 -32x -84 +92
= 4x^3 +8x^2 +10x +8 . . . . . the original dividend, as required
