Pregunta
Use the polynomials to find the specified sums and differences. \( \begin{array}{l}f(x)=\left(3 x^{4}+5 x^{2}-1\right) \\ g(x)=\left(2 x^{3}+x\right) \\ h(x)=\left(-6 x^{5}-2 x+13\right) \\ k(x)=\left(4 x^{5}+3 x^{2}+x-9\right) \\ m(x)=\left(x^{4}-9\right) \\ p(x)=\left(x^{4}+9\right) \\ \quad m(x)-p(x)\end{array} \)
Ask by Graham Erickson. in the United States
Jan 29,2025
Solución de tutoría real
Respuesta verificada por el tutor
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\( m(x) - p(x) = -18 \)
Solución
To find the difference between the polynomials \( m(x) \) and \( p(x) \), we perform the following subtraction:
\[
m(x) - p(x) = \left( x^4 - 9 \right) - \left( x^4 + 9 \right)
\]
Let's simplify step by step:
1. **Distribute the negative sign** across the terms in \( p(x) \):
\[
m(x) - p(x) = x^4 - 9 - x^4 - 9
\]
2. **Combine like terms**:
\[
x^4 - x^4 - 9 - 9 = 0x^4 - 18 = -18
\]
**Final Answer:**
\[
m(x) - p(x) = -18
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Bonus Knowledge
To find \( m(x) - p(x) \), we need to start with the given polynomials: \( m(x) = x^{4} - 9 \) \( p(x) = x^{4} + 9 \) Now, we compute the difference: \[ m(x) - p(x) = (x^{4} - 9) - (x^{4} + 9) \] Distributing the negative sign gives us: \[ = x^{4} - 9 - x^{4} - 9 \] The \( x^{4} \) terms cancel out: \[ = -9 - 9 \] Combining the constant terms results in: \[ = -18 \] So the final result for \( m(x) - p(x) \) is: \[ \boxed{-18} \]
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