Question

4y^2-28y+49factor each polynomial completely.If polynomial Prime, state this.

Answer 1

We are given the following polynomial

`4y^2-28y+49`

Let us factor out the above polynomial.

We need to break the middle term into two numbers such that their sum is equal to -28 and their product is equal to 196

How about -14 and -14?

-14 -14 = -28

-14×-14 = 196

`\begin{gathered} 4y^2-28y+49 \\ 4y^2-14y-14y+49 \\ (4y^2-14y)+(-14y+49) \\ 2y(2y-7)-7(2y-7) \\ (2y-7)(2y-7) \\ (2y-7)^2 \end{gathered}`

As you can see, the polynomial is completely factored.

Also, notice that the polynomial is not a prime since it has more than 2 factors.