Question

Identify A and B, factor completely and find the real roots

Answer 1

The given equation is:

$x^3+64=0$

The equation is a sum of two(2) cubes which can be further simplified to be:

$x^3+4^3=0$

i) Hence, a=x and b=4

Factorization of sum of two(2) cubes is given by the equation;

$x^3+y^3=(x+y)(x^2-xy+y^2)$

Relating this to the given equation, we have:

$\begin{gathered} x^3+64=0 \\ x^3+4^3=0 \\ \Rightarrow(x+4)(x^2-4x+16)=0 \end{gathered}$

ii) Hence, the factor completely is:

$(x+4)(x^2-4x+16)=0$

iii) To find the real root,we have;

$\begin{gathered} x+4=0 \\ x=-4 \end{gathered}$

Hence, the real root is x = -4