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. (y-2)(y^2-4y-9) This simplifies to: AnswerThe degree of our simplified answer is:

Answer 1

The expression is given as,

`(y-2)(y^2-4y-9)`

Consider the property of indices,

`x^m\cdot x^n=x^(m+n)`

Use this property to resolve the given product,

`\begin{gathered} =y(y^2-4y-9)-2(y^2-4y-9) \\ =(y\cdot y^2)-(y\cdot4y)-(y\cdot9)-(2\cdot y^2)+(2\cdot4y)+(2\cdot9) \\ =y^3-4y^2-9y-2y^2+8y+18 \\ =y^3-6y^2-y+18 \end{gathered}`

Thus, the simplified form of the given product of polynomial is obtained as,

`y^3-6y^2-y+18`

Since the highest integral exponent of the variable, 'y' in the expression is equal to 3.

Therefore, the degree of the obtained polynomial is also 3.

Thus, it can be concluded that -

The product simplifies to,

`y^3-6y^2-y+18`

The degree of our simplified expression is 3.