Find the quotient. (5x⁴ - 3x² + 4) ÷ (x + 1)

Solution:

Given (5x⁴ - 3x² + 4) ÷ (x + 1)

To find the solution, we need to use r`

Here, divisor is x + 1 and dividend is (5x⁴ - 3x² + 4)

x + 1) 5x⁴ + 0x³ - 3x² + 0x + 4 (5x³ - 5x² + 2x - 2
      (-) 5x4 + 5x³
        ----------------------------------
                  -5x³ - 3x²
        (-)      -5x³ - 5x²
        ----------------------------------
                          2x² + 0x
                (-)     2x² + 2x
           -------------------------------
                                  -2x + 4
                  (-)            -2x - 2
          ---------------------------------
                                          6

The remainder is 6 and the quotient is 5x³ - 5x² + 2x - 2

Find the quotient. (5x⁴ - 3x² + 4) ÷ (x + 1)

Summary:

The quotient when (5x⁴ - 3x² + 4) ÷ (x + 1) is 5x³ - 5x² + 2x - 2.