Answer :
The quotient is 7x⁵ + 14x⁴ + 24x³ + 48x² + 98x + 196 and the remainder is 405.
To find the quotient and remainder when [tex]\(7x^6 - 5x^4 + 7x^2 + 5\)[/tex] is divided by x - 2, we'll use synthetic division.
Step 1: Set up the synthetic division table with the coefficients of the polynomial:
7, 0, -5, 0, 7, 0, 5
Step 2: Since we're dividing by x - 2, we'll use 2 as the divisor.
Step 3: Perform synthetic division:
Step 4: The final result in the last row gives us the coefficients of the quotient:
[tex]\[7x^5 + 14x^4 + 24x^3 + 48x^2 + 98x + 196\][/tex]
Step 5: The remainder is found in the last entry of the bottom row, which is 405.
