Divide x^2+3x-18 by x-3
To divide the polynomial \(x^2 + 3x - 18\) by \(x - 3\), we can use the long division method. Here's how you can do it step by step:
Step 1: Arrange the terms of the dividend in descending order of their exponents. In this case, we have \(x^2 + 3x - 18\).
Step 2: Divide the first term of the dividend by the first term of the divisor. Divide \(x^2\) by \(x\) to get \(x\). Write this result above the horizontal line.
Step 3: Multiply the divisor by the result obtained in Step 2. Multiply \((x - 3)\) by \(x\) to get \(x^2 - 3x\). Write this product below the dividend, aligning it with the corresponding terms.
```
x
___________
x - 3 | x^2 + 3x - 18
```
```
x
___________
x - 3 | x^2 + 3x - 18
- (x^2 - 3x)
___________
6x - 18
```
Step 4: Subtract the result from Step 3 from the corresponding terms of the dividend. Subtract \((x^2 - 3x)\) from \((x^2 + 3x)\) to get \(6x\), and subtract \(-18\) from \(-18\) to get \(0\). Write the result below the horizontal line.
```
x
___________
x - 3 | x^2 + 3x - 18
- (x^2 - 3x)
___________
6x - 18
- (6x - 18)
___________
0
```
Step 5: Check if there are any remaining terms in the dividend. In this case, there are no remaining terms.
Step 6: Write the final result. The quotient is \(x\) and the remainder is \(0\). Therefore, \(x^2 + 3x - 18\) divided by \(x - 3\) equals \(x\), with no remainder.
The final division is \(x^2 + 3x - 18 = (x - 3)(x)\).