Questions: A rock is dropped from the top of a 256-foot cliff. The height, in feet, of the rock above the water after t seconds is modeled by the polynomial 256-16 t^2. Factor this expression completely. 256-16 t^2=

A rock is dropped from the top of a 256-foot cliff. The height, in feet, of the rock above the water after t seconds is modeled by the polynomial 256-16 t^2. Factor this expression completely.

256-16 t^2=

Transcript text: A rock is dropped from the top of a 256-foot cliff. The height, in feet, of the rock above the water after $t$ seconds is modeled by the polynomial $256-16 t^{2}$. Factor this expression completely. \[ 256-16 t^{2}= \]

Solution

Solution Steps

Step 1: Find the greatest common factor (GCF)

The GCF of 256 and 16 is 16.

Step 2: Factor out the GCF

Factoring out 16 from the expression 256 - 16t² gives 16(16 - t²).

Step 3: Factor the difference of squares

The expression inside the parentheses, 16 - t², is a difference of squares. It can be factored as (4 - t)(4 + t).

Final Answer:

16(4 - t)(4 + t)

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!