Let p be the quartic (degree 4) polynomial that satisfies p(i) = 2, i = 0,1,...

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Let p be the quartic (degree 4) polynomial that satisfies p(i) = 2ª, i = 0,1, 2, 3, 4. Then p(x) Hint: You may have a better idea, but a brute force approach is to write = p(x) = ax¹ + bx³ + cx² + dx + e where a, b, c, d, and e, are the unknown coefficients, and then solve the linear system p(0) = 1, p(1) = 2, p(2) = 4, p(3) = 8, and p(4) = 16 for a, b, c, d, and e. Let p be the quartic (degree 4) polynomial that satisfies p(i) = 2ª, i = 0,1, 2, 3, 4. Then p(x) Hint: You may have a better idea, but a brute force approach is to write = p(x) = ax¹ + bx³ + cx² + dx + e where a, b, c, d, and e, are the unknown coefficients, and then solve the linear system p(0) = 1, p(1) = 2, p(2) = 4, p(3) = 8, and p(4) = 16 for a, b, c, d, and e.