Answer:
4x² +3x -5 (no remainder)
Explanation:
You want the quotient and remainder from the long division ...
(8x³ -6x² -19x +15) ÷ (2x -3)
Long division
The attachment shows the tableau for the long division. There is no remainder.
Steps
Long division of polynomials is substantially similar to long division of numbers. The quotient term at any stage is found by dividing leading dividend term by the leading divisor term.
As in numerical long division, the quotient term is then multiplied by the divisor, and that product is subtracted from the dividend to get a new dividend. The process repeats until the degree of the dividend is less than the degree of the divisor.
The quotient and product at each stage are shown in the "Hints" column of the attachment.
The quotient is 4x² +3x -5. There is no remainder.
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