Find a degree 3 polynomial that has zeros − 1 , 1 and 5 and in which the coefficient of x ^ 2 is − 10 .

Question

Can I get some help with this please.

Answer 1

P(x)= -10 (x+1)(x-1)(x-5)

Answer 2

If -1, 1 and 5 are zeros, then (x + 1),(x - 1) and (x - 5) must be factors.

Now we multiply the factors together: (x + 1)(x - 1)(x - 5) .

(x + 1)(x - 1) = x² -1

(x² -1 )(x - 5) = x³ - 5x² - x + 5

To get the coefficient of the x² term to be -10, we need to multiply -5 times 2 so we multiply all the coefficients and constant by 2.

That give us the polynomial 2x³ - 10x² - 2x + 10