Question

Use the long division method to find the result when 3, x, cubed, plus, 13, x, squared, plus, 15, x, plus, 23x

3
+13x
2
+15x+2 is divided by x, plus, 2x+2.

Answer 1

To divide the polynomial 3x³ + 13x² + 15x + 2 by x + 2x + 2 using the long division method, divide the terms in the polynomial and subtract them from the original polynomial until there are no more terms or the degree of the resulting polynomial is less than the degree of the divisor. The final result is the quotient 3x² + 7x + 1.

Step-by-step explanation:

To divide the polynomial 3x³ + 13x² + 15x + 2 by x + 2x + 2 using the long division method, follow these steps:

1. Divide the first term 3x³ by the leading term x, which gives 3x².
2. Multiply the divisor x + 2x + 2 by the quotient 3x², which gives 3x³ + 6x² + 6x.
3. Subtract this result 3x³ + 6x² + 6x from the original polynomial 3x³ + 13x² + 15x + 2, which gives 7x² + 9x + 2.
4. Repeat the process with the new polynomial 7x² + 9x + 2.

The division process continues until there are no more terms left or the degree of the resulting polynomial is less than the degree of the divisor. The final result after performing all the steps in the long division method is the quotient 3x² + 7x + 1.