Question

Solve the cubic equation :

$x^3+x^2-16x=16$

• A. $x=-1,\pm 4$
• B. $x=2,\pm 3$
• C. $x=1,\pm 2$
• D. $x=2,\pm 1$

Answer 1

The correct option is A $x=-1,\pm 4$

$x^3+x^2-16x=16$

$x^3+x^2-16x-16=0$

Let $a\left(x\right)=x^3+x^2-16x-16$

$a(-1)=(-1{)}^3+(-1{)}^2-16(-1)-16=-1+1+16-16=0$

Therefore, $a\left(x\right)=(x+1)(x^2-16)$

$0=(x+1)(x-4)(x+4)$

$x=-1,4,-4$