Find the quotient and remainder using long division. \[ \frac{10 x^{2}+28 x+18}{2 x+4} \] The quotient is The remainder is Question Help: Video Submit Question Jump to Answer
Solution
Step 1 ：Divide the first term of the numerator (10x^2) by the first term of the denominator (2x) to get 5x. This is the first term of our quotient.
Step 2 ：Multiply the entire denominator (2x + 4) by the first term of our quotient (5x) to get 10x^2 + 20x.
Step 3 ：Subtract this from our original numerator (10x^2 + 28x + 18) to get a new numerator of 8x + 18.
Step 4 ：Divide the first term of our new numerator (8x) by the first term of the denominator (2x) to get 4. This is the second term of our quotient.
Step 5 ：Multiply the entire denominator (2x + 4) by the second term of our quotient (4) to get 8x + 16.
Step 6 ：Subtract this from our new numerator (8x + 18) to get a remainder of 2.
Step 7 ：So, the quotient is \(5x + 4\) and the remainder is \(2\).
Step 8 ：Check the work. Multiply the quotient \((5x + 4)\) by the denominator \((2x + 4)\) and add the remainder \((2)\), we should get the original numerator \((10x^2 + 28x + 18)\).
Step 9 ：\((5x + 4)(2x + 4) + 2 = 10x^2 + 20x + 8x + 16 + 2 = 10x^2 + 28x + 18\)
Step 10 ：So, the answer is correct. The final answer is \(\boxed{5x + 4}\) with a remainder of \(\boxed{2}\).
