Thornton Garza
07/28/2024 · Middle School
Given that \( f(x)=x^{2}+6 x-27 \) and \( g(x)=x-3 \), find \( f(x) \cdot g(x) \) and express the result as a polynomial in simplest form.
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Calculate or simplify the expression \( (x^2+6x-27)*(x-3) \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(x^{2}+6x-27\right)\left(x-3\right)\)
- step1: Multiply the expression:
\(\left(x+9\right)\left(x-3\right)^{2}\)
- step2: Rearrange the terms:
\(\left(x-3\right)^{2}\left(x+9\right)\)
- step3: Expand the expression:
\(\left(x^{2}-6x+9\right)\left(x+9\right)\)
- step4: Apply the distributive property:
\(x^{2}\times x+x^{2}\times 9-6x\times x-6x\times 9+9x+9\times 9\)
- step5: Multiply the terms:
\(x^{3}+9x^{2}-6x^{2}-54x+9x+81\)
- step6: Subtract the terms:
\(x^{3}+3x^{2}-45x+81\)
The result of \( f(x) \cdot g(x) \) is \( x^{3}+3x^{2}-45x+81 \).
Quick Answer
\( f(x) \cdot g(x) = x^{3}+3x^{2}-45x+81 \)
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