Question

Which of the following is a polynomial with roots 4,6, and -7?

Answer 1

the polynomial would be:
P(x)=(x-4)(x-6)(x+7)
P(x)=(x²-6x-4x+24)(x+7)
P(x)=(x²-10x+24)(x+7)
P(x)=x³+7x²-10x²-70x+24x+168
P(x)=x³-3x²-46x+168

Answer: P(x)=x³-3x²-46x+168

Answer 2

P(x)= x³ - 3 x² - 46 x +168

Explanation:

given roots of the polynomial are given as (4,6, -7)

hence the polynomial will be equal to

P(x) = (x-4) (x-6) (x+7)

P(x) = (x-4) (x²+7 x -6 x -42)

P(x) = (x-4) (x²+x -42)

P(x) = x³ + x²-42 x -4 x² -4 x +168

P(x) = x³ - 3 x² - 46 x +168

hence, the required polynomial is P(x) = x³ - 3 x² - 46 x +168