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Section 2.2
64, 68, & 70
For 64, x_1 = -sqrt{2}, x_2 = sqrt{2}
f(x) = (x - x_1)(x - x_2)
f(x) = (x - (-sqrt{2})(x - sqrt{2})
f(x) = (x + sqrt{2})(x - sqrt{2})
f(x) = x^2 -xsqrt{2} + xsqrt{2} - 2
f(x) = x^2 - 2
For 68, x_1 = -4, x_2 = -1
f(x) = (x - x_1)(x - x_2)
f(x) = (x -(-4))(x - (-1))
f(x) = (x + 4)(x + 1)
f(x) = x^2 + x + 4x + 4
f(x) = x^2 + 5x + 4
For 70, x_1 = -1, x_2 = 4, x_3 = 7, x_4 = 8
f(x) = (x - x_1)(x - x_2)(x - x_3)(x - x_4)
f(x) = (x -(-1))(x - 4)(x - 7)(x - 8)
f(x) = (x + 1)(x - 4)(x - 7)(x - 8)
f(x) = (x^2 - 3x - 4)(x^2 - 15x + 56)
f(x) = x^4 - 18x^3 + 97x^2 - 108x - 224
You say?
64, 68, & 70
For 64, x_1 = -sqrt{2}, x_2 = sqrt{2}
f(x) = (x - x_1)(x - x_2)
f(x) = (x - (-sqrt{2})(x - sqrt{2})
f(x) = (x + sqrt{2})(x - sqrt{2})
f(x) = x^2 -xsqrt{2} + xsqrt{2} - 2
f(x) = x^2 - 2
For 68, x_1 = -4, x_2 = -1
f(x) = (x - x_1)(x - x_2)
f(x) = (x -(-4))(x - (-1))
f(x) = (x + 4)(x + 1)
f(x) = x^2 + x + 4x + 4
f(x) = x^2 + 5x + 4
For 70, x_1 = -1, x_2 = 4, x_3 = 7, x_4 = 8
f(x) = (x - x_1)(x - x_2)(x - x_3)(x - x_4)
f(x) = (x -(-1))(x - 4)(x - 7)(x - 8)
f(x) = (x + 1)(x - 4)(x - 7)(x - 8)
f(x) = (x^2 - 3x - 4)(x^2 - 15x + 56)
f(x) = x^4 - 18x^3 + 97x^2 - 108x - 224
You say?