Question

Write a polynomial of least degree with rational coefficients, a leading coefficient of 1, and zeros at 3 and sqr root 7. Expand your answer and write it in standard form

Answer 1

(x-3)(x^2-7) = x^3 -3x^2 -7x + 21

just change the sign of the root and put x in front of it, then multiply the factors all together

(x-3)(x-sqr7)(x+sqr7) roots come in conjugate pairs to eliminate irrational coefficients

(x-sqr7)(x+sqr7) = x^2-7. similar to (a-b)(a+b) = a^2-b^2

Explanation: