Question

P(x)=2x3+2x2 4x 6 d(x)=x+4 p(x)÷by d(x) then find quofient and remainder

Answer 1

The quotient of
`\(P(x) = 2x^3 + 2x^2 - 4x + 6\)` divided by D(x) = x + 4 is
`\(2x^2 - 2x + 1\)`, and the remainder is -74.

To find the quotient and remainder when
`\( P(x) = 2x^3 + 2x^2 - 4x + 6 \)` is divided by
`\( D(x) = x + 4 \)`, perform polynomial long division.

Here's the process:

```

2x^2 - 2x + 1

__________________

x + 4 | 2x^3 + 2x^2 - 4x + 6

- (2x^3 + 8x^2)

_______________

-6x^2 - 4x

+ 6x^2 + 24x

______________

20x + 6

- (20x + 80)

______________

-74

```

Therefore, the quotient is
`\(2x^2 - 2x + 1\)` and the remainder is -74. The division can be expressed as:

`\[ P(x) = (2x^2 - 2x + 1)(x + 4) - 74 \]`

So, the quotient is
`\(2x^2 - 2x + 1\)` and the remainder is -74.