Question

Simplify by finding the product of the polynomials below. Then Identify the degree of your answer. When typing your answer use the carrot key ^ (press shift and 6) to indicate an exponent. Type your terms in descending order and do not put any spaces between your characters. (4t-7)^2(2t+1)-(4t^2+2t+11) This simplifies to: AnswerThe degree of our simplified answer is: Answer

Answer 1

We have the next polynomial

`\mleft(4t-7\mright)^2\mleft(2t+1\mright)-\mleft(4t^2+2t+11\mright)`

First, we solve the square

`(16t^2-56t+49)(2t+1)-\mleft(4t^2+2t+11\mright)`

Then we do the product of polynomials

`32t^3-112t^2+98t+16t^2-56t+49-4t^2-2t-11`

Then we sum like terms

`\begin{gathered} 32t^3-112t^2+16t^2-4t^2+98t-2t-56t+49-11 \\ \end{gathered}`
`\begin{gathered} 32t^3-100t^2+40t+38 \\ \end{gathered}`

ANSWER

`32t^3-100t^2+40t+38`

The degree of the polynomial is 3