Question

Use synthetic division to find the quotient and remainder when 5 x⁶-9 x⁴+6 x²+1 is divided by x-2. The quotient is The remainder is

Answer 1

Using synthetic division with the polynomial 5x^6 - 9x^4 + 6x^2 + 1 divided by x - 2, we find that the quotient is 10x^5 + 20x^4 - 49x^3 - 98x^2 + 195x + 390, and the remainder is 781.

Step-by-step explanation:

To use synthetic division to find the quotient and remainder when 5 x⁶ - 9 x⁴ + 6 x² + 1 is divided by x - 2, we set up the division as follows:

1. Write down the coefficients of the polynomial: 5, 0 (for x⁵), 0 (for x³), -9, 0 (for x), 6, 1.
2. Bring down the leading coefficient (5) as the first number in our quotient.
3. Multiply the divider's root (which is 2 in x-2) by the number just written below the line (5 in this case), and place this result (10) under the next coefficient.
4. Add the numbers in the second column: 0 + 10 = 10.
5. Repeat this process for all columns.

The final numbers below the division will represent the coefficients of the quotient polynomial and the last number will be the remainder: 10 x⁵ + 20 x⁴ - 49 x³ - 98 x² + 195 x + 390 with a remainder of 781.

In this case, the synthetic division reveals that the quotient is 10 x⁵ + 20 x⁴ - 49 x³ - 98 x² + 195 x + 390 and the remainder is 781.