Question

Which of the following is a polynomial with roots 5,7 and -8

Answer 1

The idea is to use the zero product property in reverse to go from the roots to the factorization. Then you expand out the polynomial using the distributive property.

x = 5 or x = 7 or x = -8

x-5 = 0 or x-7 = 0 or x+8 = 0

(x-5)(x-7)(x+8) = 0

(x-5)(x^2+x-56) = 0

x(x^2+x-56) - 5(x^2+x-56) = 0

x^3+x^2-56x -5x^2-5x+280 = 0

x^3-4x^2-61x+280 = 0

f(x) = x^3 - 4x^2 - 61x + 280

Answer: Choice D

Answer 2

The correct answer is option 4). x³- 4x² -61x + 280

Explanation:

It is given that, a polynomial with roots 5,7 and -8

To find the polynomial

The roots are 5,7 and -8

Then the factors are, (x-5), (x-7) and (x+8)

p(x) = (x-5)(x-7)(x+8) = (x-5)(x² + 8x -7x + 56)

= (x-5)(x² + x - 56)

= x³ + x² - 56x -5x² - 5x + 280

= x³- 4x² -61x + 280

Therefore the polynomial is p(x) = x³- 4x² -61x + 280

The correct answer is option 4). x³- 4x² -61x + 280