Write a polynomial of least degree with roots 1 and 8. Write your answer using the variable x and in standard form with a leading coefficient of 1.

Answer 1

If a polynomial has 2 roots, the least degree it could have is 2. If a polynomial has roots 1 and 8, then it has factors of (x - 1) and (x - 8). And if it has a leading coefficient of 1, then it must be:

f(x) = 1(x - 1)(x - 8)

To write it in standard form means to multiply it out and put the highest degree first and then each term in descending order (based on the exponent). So:

f(x) = x² - 9x + 8