If p=4 x^3+x-2, q=x^2-1, and r=3 x-5, then what is 2 p-(q+r) ? (A) 7 x^3-x+2 (B)

step 1 So the question gives me some expressions for p, q, and r, and then it asks me to evaluate 2p mi

If p=4 x^3+x-2, q=x^2-1, and r=3 x-5, then what is 2 p-(q+r)...

If $p=4 x^{3}+x-2, q=x^{2}-1,$ and $r=3 x-5,$ then
what is $2 p-(q+r) ?$
\begin{equation}
\begin{array}{l}{\text { (A) } 7 x^{3}-x+2} \\ {\text { (B) } 8 x^{3}-x^{2}-x+2} \\ {\text { (C) } 8 x^{3}-x^{2}-x-10} \\ {\text { (D) } 8 x^{3}-x^{2}+5 x-8}\end{array}
\end{equation}

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Key Concepts

Polynomial Scaling

This concept involves multiplying a polynomial by a constant. Each term in the polynomial is multiplied by that constant, which is essential for operations like 2p where every term in p is doubled.

Polynomial Addition and Subtraction

This is the process of adding or subtracting two or more polynomials. It requires careful distribution of any negative signs and aligning terms of the same degree, as seen in the operation 2p - (q + r).

Combining Like Terms

After performing arithmetic operations on the polynomials, terms with the same variables raised to the same power need to be consolidated. This simplifies the expression by adding or subtracting the coefficients of these like terms to produce a final, simplified form.

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