Find Polynomial of Degree n...2

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?

 

correct

 

Finally correct.