Answer :
Final answer:
Using synthetic division to divide 6x^4 - 2x^3 - 3x^2 - x by x - 5 results in Option A: 6x^3 - 28x^2 + 137x - 682. This process involves systematically breaking down the polynomial using the divisor's root and calculating the quotient.
Explanation:
The student has asked to use synthetic division to divide 6x^4 - 2x^3 - 3x^2 - x by x - 5.
To perform synthetic division, first, identify the coefficient of x in the divisor,
which here is -5 since x - 5 can be written as x + (-5).
The coefficients for the dividend are 6 (for x^4), -2 (for x^3), -3 (for x^2), -1 (for x), and don't forget the constant term, which in this case is 0 (since there's no constant term in the given polynomial).
Next, bring down the 6. Multiply 6 by -5 to get -30,
add this to -2 to get -32, and continue the process.
When these steps are followed correctly,
the quotient obtained is 6x^3 - 28x^2 + 137x - 682, and there's a remainder,
which is ignored in this context,
so the complete division result is Option A: 6x^3 - 28x^2 + 137x - 682.
