Question
8. [-/1 Points] DETAILS MY NOTES TGEIALG6 5.8.000. Perform the division. (Simplify your answer completely.) \( \left(x^{2}+10 x+32\right) \div(x+6) \) SUBMIT ANSWER
Ask by Edwards Guerrero. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The division simplifies to \( x + 4 + \frac{8}{x+6} \).
Solution
Calculate or simplify the expression \( (x^2+10x+32)/(x+6) \).
Divide the polynomials by following steps:
- step0: Using Long Division to Divide Polynomials:
\(\frac{\left(x^{2}+10x+32\right)}{\left(x+6\right)}\)
- step1: Calculate:
\(x+4+\frac{8}{x+6}\)
The result of the division \( \left(x^{2}+10 x+32\right) \div(x+6) \) is \( x+4+\frac{8}{x+6} \).
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Simplify this solution The Deep Dive
To perform the division of \( (x^{2}+10x+32) \div (x+6) \), you can use polynomial long division. First, divide the leading term \( x^2 \) by \( x \) to get \( x \). Multiply \( x \) by \( (x + 6) \) to yield \( x^2 + 6x \). Next, subtract this from the original polynomial: \[ (x^2 + 10x + 32) - (x^2 + 6x) = 4x + 32 \] Now, repeat the process. Divide \( 4x \) by \( x \) to get \( 4 \). Multiply \( 4 \) by \( (x + 6) \) to yield \( 4x + 24 \). Subtract again: \[ (4x + 32) - (4x + 24) = 8 \] So, the remainder is \( 8 \). The final result of the division is: \[ x + 4 + \frac{8}{x + 6} \] This is the simplified answer!
