Answer :
Using synthetic division, we determined the quotient to be [tex]6x^3 + 28x^2 + 163x + 978[/tex] and the remainder to be -582 when dividing f(x) by g(x). a) Quotient is 6x³ + 28x² + 163x + 978, Remainder is -582
To find the quotient and remainder of[tex]f(x) = 6x^4 - 8x^3 - 5x^2 - 6x + 6[/tex] when divided by g(x) = x - 6 using synthetic division, we follow these steps:
Write down the coefficients of f(x): 6, -8, -5, -6, and 6.- Place the zero of g(x), which is 6, in a box to the left of these coefficients.
- Bring down the first coefficient (6) to the bottom row.
- Multiply the number in the box (6) by the number just brought down (6) and put this number under the next coefficient (-8).
- Add the numbers in the second column and place the result in the bottom row. Repeat this process for the remaining coefficients.
- The bottom row, except the last number, represents the coefficients of the quotient[tex]6x^3 + 28x^2 + 163x + 978.[/tex]
- The last number in the bottom row is the remainder, -582.
Therefore, the quotient is [tex]6x^3 + 28x^2 + 163x + 978[/tex]and the remainder is -582, which corresponds to option (a).
