Question

A paper airplane is thrown off a 64-foot bridge into the water below. Its height, in feet, is represented by f(x) = –16(x^2  – 3x – 4), where x is the number of seconds since the airplane was thrown. The height of the airplane is 0 feet when it hits the water. Factor the polynomial expression –16(x^2 – 3x – 4).

Answer 1

Here are the steps in factoring the given polynomial.

`f(x)=-16(x^2-3x-4)`

Disregard -16 because it has already been factored out. Focus on the quadratic equation inside the parenthesis.

1. Find the factors of the constant term -4 that add up to the middle term -3.

a. -1 and 4 → sum is 3

b. -4 and 1 → sum is -3

2. As we can see above, the factors of -4 that add up to -3 are -4 and 1. Hence, the quadratic equation can be factored to:

`(x^2-3x-4)=(x-4)(x+1)`

So, the polynomial expression when factored is f(x) = (-16)(x - 4)(x + 1).

`f(x)=(-16)(x-4)(x+1)`