Simplify. (x^2-3x-10)/(x+2)
How?
(I don't have any answers for this one)
To simplify the expression (x^2 - 3x - 10)/(x + 2), you can start by factoring the numerator if possible. The numerator can be factored as (x - 5)(x + 2). So, now the expression becomes ((x - 5)(x + 2))/(x + 2).
Next, you can cancel out the common factor of (x + 2) in the numerator and denominator. This leaves you with (x - 5).
Therefore, the simplified form of (x^2 - 3x - 10)/(x + 2) is x - 5.
To simplify the given expression (x^2-3x-10)/(x+2), you need to perform polynomial division or factorization. Let's go through both methods step by step.
1. Polynomial division (long division):
Start by dividing the polynomial x^2-3x-10 by the binomial x+2.
x-5
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x+2 | x^2 - 3x - 10
Perform the division by considering the leading term of the dividend (x^2) and the leading term of the divisor (x). Divide x^2 by x, which gives x, and then multiply x by (x+2) to get x^2 + 2x. Subtract this result from the original dividend: (x^2 - 3x - 10) - (x^2 + 2x) = -5x - 10.
Now, we need to divide -5x - 10 by x+2. Divide -5x by x, which is -5, and then multiply -5 by (x+2) to get -5x - 10. Subtract this result from the remainder: (-5x - 10) - (-5x - 10) = 0.
Hence, the result of the division is x-5, which means (x^2-3x-10)/(x+2) = x-5.
2. Factorization:
If you're familiar with factoring polynomials, you can use that method as well.
The expression (x^2-3x-10)/(x+2) can be factored as [(x-5)(x+2)]/(x+2).
Notice that (x+2) is common in the numerator and denominator of the expression, so it can be canceled out.
This leaves us with (x-5), which is the simplified form of the original expression.
Therefore, the simplified form of (x^2-3x-10)/(x+2) is x-5.
better get good at factoring.
x^2-3x-10 = (x+2)(x-5)
now divide out the x+2