Question

a ball is thrown upward from an initial height of 40 feet with an initial velocity of 12 feet per second. after t seconds, the height of the ball can be described by the polynomial $-16t^{2}+12t + 40$.
step 2 of 2: completely factor the polynomial $-16t^{2}+12t + 40$.

Explanation:

Step1: Factor out the greatest common factor

The greatest common factor of \(-16t^{2}\), \(12t\), and \(40\) is \(-4\).

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Step2: Factor the quadratic expression inside the parentheses

For the quadratic \(4t^{2}-3t - 10\), we need to find two numbers \(a\) and \(b\) such that \(a\times b=4\times(- 10)=-40\) and \(a + b=-3\). The numbers are \(5\) and \(-8\).

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Answer:

\(-4(4t + 5)(t - 2)\)