Question

x^2+16x+64 factor polynomial completely if polynomial is prime state this

Answer 1

(x + 8)(x + 8)

Explanation:$x^2\text{ + 16x + 64}$

factors of 64 whose sum gives 16: +8 and +8

$\begin{gathered} 8\text{ + 8 = 16} \\ 8(8)\text{ = 64} \\ x^2\text{ + 8x + 8x + 64} \end{gathered}$

factorise:

$\begin{gathered} x(x\text{ + 8) + 8(x + 8)} \\ (x\text{ + 8)(x + 8)} \\ \\ A\text{ polynomial is only prime if it not factorisable with an whole number.} \\ \text{This is a reducible polynomial (factorisable). Hence, not a prime} \end{gathered}$

Hence, the factorised form:

(x + 8)(x + 8)