Determine the appropriate numbers or variables to fill in the blanks that will correctly represent the synthetic division problem: Fill in the blanks to correctly complete the sentence. To perform the division $x - 3 \longdiv { x ^ { 3 } + 4 x ^ { 2 } + 2 x }$, begin by writing the synthetic division problem shown below. \[ \square \longdiv { 1 \square . 2 \square } \]

Step 1 ：Write the division problem in long division format: \(x - 3\) into \(x^3 + 4x^2 + 2x\)

Step 2 ：Divide the first term in the dividend (\(x^3\)) by the first term in the divisor (\(x\)), to get \(x^2\)

Step 3 ：Multiply the divisor (\(x - 3\)) by the result from step 2 (\(x^2\)), to get \(x^3 - 3x^2\)

Step 4 ：Subtract the result from step 3 (\(x^3 - 3x^2\)) from the first two terms of the dividend (\(x^3 + 4x^2\)), to get \(7x^2\)

Step 5 ：Bring down the next term from the dividend (\(2x\)), to get \(7x^2 + 2x\)

Step 6 ：Repeat steps 2-5 with the new dividend (\(7x^2 + 2x\)), to get \(7x\) and \(21x^2 - 6x\)

Step 7 ：Subtract \(21x^2 - 6x\) from \(7x^2 + 2x\), to get \(-14x^2 + 8x\)

Step 8 ：The divisor (\(x - 3\)) does not divide evenly into the new dividend (\(-14x^2 + 8x\)), so the remainder is \(-14x^2 + 8x\)

Step 9 ：The final result of the division is the quotient (\(x^2 + 7x\)) plus the remainder (\(-14x^2 + 8x\)) divided by the divisor (\(x - 3\))

Step 10 ：So, \(x^3 + 4x^2 + 2x\) divided by \(x - 3\) is \(x^2 + 7x - \frac{{14x^2 + 8x}}{{x - 3}}\)