division
(x to da 2nd power + x - 6) / (x - 2)= ?
To simplify the given expression, (x^2 + x - 6) / (x - 2), we can use polynomial division or factorization.
Let's use polynomial division to find the quotient. Here's how you can proceed:
Step 1: Arrange the expression in descending order of powers of x.
(x^2 + x - 6) / (x - 2)
Step 2: Divide the term with the highest power of x (x^2) by the term with the highest power of x in the divisor (x). The result is the first term of the quotient.
The first term of the quotient is x.
Step 3: Multiply the divisor (x - 2) by the first term of the quotient (x), and subtract the result from the dividend (x^2 + x - 6).
(x^2 + x - 6) - x(x - 2)
Simplifying, we get:
(x^2 + x - 6) - (x^2 - 2x)
Combining like terms:
x^2 + x - 6 - x^2 + 2x
Simplifying further:
3x - 6
Step 4: Repeat steps 2 and 3 with the new expression (3x - 6) as the dividend.
The second term of the quotient is 3.
Step 5: Multiply the divisor (x - 2) by the second term of the quotient (3), and subtract the result from the new dividend (3x - 6).
(3x - 6) - 3(x - 2)
Simplifying, we get:
3x - 6 - (3x - 6)
Combining like terms:
0
Since the result is 0, there is no remainder.
Step 6: Write the quotient obtained.
The quotient is x + 3.
Therefore, (x^2 + x - 6) / (x - 2) simplifies to x + 3.