Divide 2 x squared plus 3 x space minus space 14 by (x-2) the result is
( 2 x^2 + 3 x - 14) / (x-2)
we know 14 is 2 * 7
so try
( 2 x^2 + 3 x - 14) = (2x+7) times something
(2x+7) (x-2) ah hah
so
( 2 x^2 + 3 x - 14) / (x-2)
is
(2x+7) (x-2) / (x-2)
or, if you are not good at factoring, just do a long division. There are several handy web sites that show the details.
To divide the expression 2x^2 + 3x - 14 by (x - 2), we can use polynomial long division. Here's how you can do it step-by-step:
Step 1: Arrange the expression in descending order.
2x^2 + 3x - 14
Step 2: Divide the first term of the expression (2x^2) by the first term of the divisor (x). Write the result above the line.
________
x - 2 | 2x^2 + 3x - 14
2x
Step 3: Multiply the divisor (x - 2) by the quotient (2x) and write the result below the dividend (2x^2 + 3x - 14).
________
x - 2 | 2x^2 + 3x - 14
2x
-----
2x^2 - 4x
Step 4: Subtract the product from the previous step (2x^2 - 4x) from the dividend (2x^2 + 3x - 14). Write the result below the line.
________
x - 2 | 2x^2 + 3x - 14
2x
-----
2x^2 - 4x
+ 3x
-----
7x - 14
Step 5: Bring down the next term from the dividend (-14) and place it next to the result.
________
x - 2 | 2x^2 + 3x - 14
2x
-----
2x^2 - 4x
+ 3x
-----
7x - 14
- 14
Step 6: Repeat steps 2-5 until there are no terms left in the dividend.
________
x - 2 | 2x^2 + 3x - 14
2x + 7
________
x - 2 | 2x^2 + 3x - 14
2x + 7
-----
7x - 14
- 14
-----
0
Step 7: When there are no terms remaining in the dividend, the quotient is 2x + 7.
Therefore, the result of dividing 2x^2 + 3x - 14 by (x - 2) is 2x + 7.