Questions: Divide and simplify (x^2+8x+15)/(x+5). Is x+5 a factor of x^2+8x+15?

Transcript text: Divide and simplify $\frac{x^{2}+8 x+15}{x+5}$. Is $\mathrm{x}+5$ a factor of $x^{2}+8 x+15$ ?

Solution

Solution Steps

To determine if $ x+5 $ is a factor of $ x^2 + 8x + 15 $, we can perform polynomial division. If the remainder is zero, then $ x+5 $ is a factor. Alternatively, we can factorize $ x^2 + 8x + 15 $ and check if $ x+5 $ is one of the factors.

Step 1: Define the Polynomial and Divisor

We start with the polynomial $ x^2 + 8x + 15 $ and the divisor $ x + 5 $.

Step 2: Perform Polynomial Division

We perform polynomial division of $ x^2 + 8x + 15 $ by $ x + 5 $.

Step 3: Check the Remainder

After performing the division, we find that the remainder is zero. This indicates that $ x + 5 $ is a factor of $ x^2 + 8x + 15 $.

Final Answer

$\boxed{x + 3}$

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