Question

Divide. 6x³+10x²-14x-19-:3x²+2x answer should give the quotient

Answer 1

The quotient of the division of 6
`x^3` + 10
`x^2` - 14x - 19 by 3
`x^2` + 2x is 2x - 4.

Step-by-step explanation:

When dividing 6
`x^3` + 10
`x^2` - 14x - 19 by 3
`x^2` + 2x, use the polynomial long division method. First, divide the highest-degree term of the dividend by the highest-degree term of the divisor. This gives 2x. Multiply the divisor by 2x and subtract it from the dividend, which leaves -4 as the remainder. The resulting quotient is 2x - 4.

In polynomial division, the process involves dividing each term of the dividend by the divisor. The first term of the quotient is found by dividing the leading term of the dividend by the leading term of the divisor, which in this case yields 2x. After multiplying the entire divisor by this term, subtracting it from the dividend gives a remainder of -4. Hence, 2x - 4 is the final quotient.

The quotient represents the result of the division of the polynomial 6
`x^3` + 10
`x^2` - 14x - 19 by 3
`x^2` + 2x. It signifies how many times the divisor fits into the dividend and the remainder left over after the division process. Therefore, 2x - 4 is the outcome of this polynomial division, indicating the solution for the given problem.