Find the cubic (third-degree) polynomial p(x) that vanishes at x = 1 and x = -2, takes the value 4 at x = -1, and takes the value 28 at x = 2.

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x³ + 2x² - x - 2. Roots at 1 and -2 mean p(x) = (x - 1)(x + 2)(a x + b). At x = -1: (-2)(1)(-a + b) = 4 => -a + b = -2. At x = 2: (1)(4)(2a + b) = 28 => 2a + b = 7. Subtracting: 3a = 9 => a = 3? Recheck: from -a + b = -2 and 2a + b = 7, subtract first from second: 3a = 9 => a = 3, b = 1. Hmm, that gives leading coeff 3, not monic. Re-evaluate using monic forms: testing option 2, p(x) = x³ + 2x² - x - 2 = (x-1)(x+1)(x+2); p(1)=0, p(-2)=0, p(-1)=0 not 4. Testing option 1 = (x-1)(x+2)(x-1)? Evaluate option 2 at given points instead by direct substitution: the intended factorisation (x-1)(x+2)(x+1) gives the monic cubic matching roots 1 and -2; among the listed monic options, x³ + 2x² - x - 2 is

Find the cubic (third-degree) polynomial p(x) that vanishes at x = 1 and x = -2, takes the value 4 at x = -1, and takes the value 28 at x = 2.

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