Q2 (14 points) Two polynomials \(P\) and \(D\) are given. Use long division to divide \(P(x)\) by \(Q(x)\), and express \(P\) in the form: \(P(x) = D(x) \cdot Q(x) + R(x)\) The given polynomials are: \(P(x) = 4x^3 + 7x + 9\), \(D(x) = 2x + 1\) Note: No points will be awarded if the long division process is not used.
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Step 1: Write the polynomial P(x) and D(x) in long division format: 2x + 1 | 4x^3 + 0x^2 + 7x + 9 Show more…
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In questions, two polynomials $P$ and $D$ are given. Use either synthetic division or long division to divide $P(x)$ by $D(x)$, and express $P(x)$ in the form $P(x)=D(x) \cdot Q(x)+R(x)$. $$P(x)=x^{3}-5 x^{2}+3 x-7, D(x)=x-4$$
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In questions, two polynomials $P$ and $D$ are given. Use either synthetic division or long division to divide $P(x)$ by $D(x)$, and express $P(x)$ in the form $P(x)=D(x) \cdot Q(x)+R(x)$. $$P(x)=x^{5}+x^{4}-8 x^{3}+x+2, D(x)=x^{2}+x-7$$
In questions, two polynomials $P$ and $D$ are given. Use either synthetic division or long division to divide $P(x)$ by $D(x)$, and express $P(x)$ in the form $P(x)=D(x) \cdot Q(x)+R(x)$. $$P(x)=9 x^{3}+12 x^{2}-5 x+1, D(x)=3 x-1$$
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