Answer :
To divide (6x³+19x²+3x−22) by (2x+3) using synthetic division, find the zero of the divisor, use it to multiply and combine the coefficients in a synthetic division table and obtain the quotient and the remainder.So the result of the division is 3x²+2x+3 with a remainder of -7.
To divide (6x³+19x²+3x-22) by (2x+3) using synthetic division, follow these steps:
- First, identify the zero of the divisor 2x+3, which is x=-3/2.
- Write down the coefficients of the dividend: 6, 19, 3, -22.
- Bring down the leading coefficient (6) to the bottom row.
- Multiply the result in the bottom row by the zero of the divisor (-3/2) and write the result under the next coefficient.
- Combine the two values in the second column and repeat the multiplication and combining steps for each column.
After completing these steps, the numbers in the bottom row will represent the coefficients of the quotient polynomial (3x²+2x+3), and the last number will be the remainder -7. So the result of the division is 3x²+2x+3 with a remainder of -7.
