Question

Divide the polynomial x4−3x3−19x2+3x+18 by the factor (x-1)(1 point) Responses x2+9x+18 x squared plus 9 x plus 18 x3−2x2−21x−18 x cubed minus 2 x squared minus 21 x minus 18 x3−2x2−21x+18

Answer 1

To divide the polynomial \( P(x) = x^4 - 3x^3 - 19x^2 + 3x + 18 \) by the factor \( (x - 1) \), we can use synthetic division or polynomial long division.

Using synthetic division:

1. We divide \( P(x) \) by \( (x - 1) \) by substituting \( x = 1 \).

The coefficients of \( P(x) \) are \( 1, -3, -19, 3, 18 \).

We perform the synthetic division:

```
1 | 1 -3 -19 3 18
| 1 -2 -21 -18
--------------------------
1 -2 -21 -18 0
```

The result is \( x^3 - 2x^2 - 21x - 18 \).

So, when \( P(x) \) is divided by \( (x-1) \), we get the quotient \( Q(x) = x^3 - 2x^2 - 21x - 18 \) with a remainder of 0.

Since we need to find the answer to the division by \( (x - 1) \), the response is:

**\( x^3 - 2x^2 - 21x - 18 \)** (or \( x3−2x2−21x−18 \)).