Question

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

Answer 1

Keywords:

Divide, polynomial, quotient, divisor, dividend, rest

For this case, we must find the quotient by dividing the polynomial
`(5x ^ 4-3x ^ 2 + 4)\ by\ (x + 1)`. We must build a quotient that, when multiplied by the divisor, eliminates the terms of the dividend until it reaches the rest, as shown in the attached figure. At the end of the division, to verify we must bear in mind that:

`Dividend = Quotient * Divider + Remainder`

Answer:

See attached image

Answer 2

`5x^3-5x^2+2x-2`

Explanation:

Since,

Dividend = Quotient × Divisor + remainder

Here, the given problem is,

`(5x^4-3x^2+4)/ (x+1)`

By the long division ( shown below),

We get,

`5x^4-3x^2+4=(5x^3-5x^2+2x-2)(x+1)+6`

Since, (x+1) is the divisor,

Thus, the Quotient of the given problem is,

`5x^3-5x^2+2x-2`