The quotient of dividing (3x⁴ - 2x³ + 7x² - 4) by (x - 3) is 3x³ + 7x² + 28x + 84 and the remainder is 248
The division expression is given as:
(3x⁴ - 2x³ + 7x² - 4) / (x - 3)
Set the divisor to 0
x - 3 = 0
Solve for x
x = 3
Substitute x = 3 in 3x⁴ - 2x³ + 7x² - 4
3x⁴ - 2x³ + 7x² - 4 = 3(3)⁴ - 2(3)³ + 7(3)² - 4
Evaluate
3x⁴ - 2x³ + 7x² - 4 = 248
This means that the remainder is 248
Recall that:
Dividend = Divisor * Quotient + Remainder
So, we have:
3x⁴ - 2x³ + 7x² - 4 = x - 3 * Q + 248
Subtract 248 from both sides
3x⁴ - 2x³ + 7x² - 252 = x - 3 * Q
Divide both sides by x - 3
Q = (3x⁴ - 2x³ + 7x² - 252)/(x - 3)
Factorize the numerator
Q = (x - 3)(3x³ + 7x² + 28x + 84)/(x - 3)
Cancel out the common factors
Q = 3x³ + 7x² + 28x + 84
Hence, the quotient is 3x³ + 7x² + 28x + 84 and the remainder is 248
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