Divide 3x3+17x2+21x−9

Question

by x+3
using synthetic division.(1 point)
Responses

3x2+26x+99 +288x+3
3x2+26x+99 +288x+3

3x2+8x−3
3 x squared plus 8 x minus 3

3x2+8x+3
3 x squared plus 8 x plus 3

3x2+8x−3−18x+3

Answer 1

To divide the polynomial \( P(x) = 3x^3 + 17x^2 + 21x - 9 \) by \( x + 3 \) using synthetic division, we can follow these steps:

1. Identify the zero of the divisor: For \( x + 3 \), the zero is \( x = -3 \).

2. Set up the synthetic division: Write down the coefficients of \( P(x) \), which are \( 3, 17, 21, -9 \).

3. Carrying out the synthetic division:

   -3 |  3   17   21   -9
      |      -9   -24   9
   -----------------------
        3    8   -3    0
   

   • Bring down the first coefficient (3).
   • Multiply -3 by 3 and write it under 17: \( -3 \times 3 = -9 \).
   • Add \( 17 + (-9) = 8 \).
   • Multiply -3 by 8: \( -3 \times 8 = -24 \), and write it under 21.
   • Add \( 21 + (-24) = -3 \).
   • Multiply -3 by -3: \( -3 \times -3 = 9 \), and write it under -9.
   • Add \( -9 + 9 = 0 \).

4. Interpret the result: The bottom row gives the coefficients of the quotient polynomial and the last number (0) is the remainder.

So, we find that the result of the division is:

\[ 3x^2 + 8x - 3 \]

Thus, the correct response is:

3x^2 + 8x - 3.