Answer :
Final answer:
To divide the polynomial 3x³+19x²+4x-12 by x+6 using synthetic division, you can follow these steps: Write the coefficients of the polynomial in descending order, change the sign of the divisor and write it as -6, perform the synthetic division, and the final row of numbers represents the coefficients of the quotient: 3, 1, -2, 0. The result when dividing 3x³+19x²+4x-12 by x+6 is 3x²+x-2.
Explanation:
To divide the polynomial 3x³+19x²+4x-12 by x+6 using synthetic division, follow these steps:
- Write the coefficients of the polynomial in descending order: 3, 19, 4, -12.
- Change the sign of the divisor and write it as -6.
- Bring down the first coefficient, 3.
- Multiply -6 by 3 to get -18, and write the result below the next coefficient.
- Add the two numbers: 19 + (-18) = 1, and write the result below the previous result.
- Multiply -6 by 1 to get -6, and write the result below the previous result.
- Add the two numbers: 4 + (-6) = -2, and write the result below the previous result.
- Multiply -6 by -2 to get 12, and write the result below the previous result.
- Add the two numbers: -12 + 12 = 0.
- The final row of numbers represents the coefficients of the quotient: 3, 1, -2, 0.
The result when 3x³+19x²+4x-12 is divided by x+6 is 3x²+x-2.
Learn more about Synthetic division here:
https://brainly.com/question/31409612
#SPJ11
