Perform the division: \((4x^3 + 3x^2 - 30x - 10) \div (x - 3)\)

The division of (4x³ + 3x² - 30x - 10) by (x - 3) is equal to 4x² + 3x - 21 with a remainder of -73.
How to divide the polynomial
To divide the polynomial (4x³ + 3x² - 30x - 10) by (x - 3), we can use long division Divide the first term of the dividend by the first term of the divisor:
4x³ / x = 4x²
4x² * (x - 3) = 4x³ - 12x²
(4x³ + 3x² - 30x - 10) - (4x³ - 12x²) = 3x²- 30x - 10
Bring down the next term from the dividend:
3x² - 30x - 10
3x² / x = 3x
Multiply the divisor (x - 3) by the result from step 5:
3x * (x - 3) = 3x² - 9x
(3x² - 30x - 10) - (3x²- 9x) = -21x - 10
Bring down the next term from the dividend:
-21x - 10
-21x / x = -21
Multiply the dvisor (x - 3) by the result from step 6:
-21 * (x - 3) = -21x + 63
(-21x - 10) - (-21x + 63) = -73
The result of the division is the sum of the quotients obtained in each step:
4x² + 3x + (-21)
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Answered by lholamidemakinde | 2024-06-17

The polynomial 4 x 3 + 3 x 2 − 30 x − 10 divided by the binomial x − 3 gives a quotient of 4 x 2 + 3 x + 21 with a remainder of 53 . The final result can be expressed as 4 x 2 + 3 x + 21 + x − 3 53 ​ .
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Answered by lholamidemakinde | 2024-11-05