Solve the cubic equation : $x^3+x^2-16x=16$
- $x=-1, \pm 4$
- $x=2, \pm 3$
- $x=1,\pm 2$
- $x=2, \pm 1$
Reveal answer
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A
Correct answer
Explanation
x^3 + x^2 - 16x - 16 = 0. x^2(x+1) - 16(x+1) = 0. (x^2-16)(x+1) = 0. (x-4)(x+4)(x+1) = 0. Roots are -1, 4, -4.
AI explanation
By moving 16 to the left side, the cubic equation becomes x^3 + x^2 - 16x - 16 = 0. We group the terms into two pairs to factor by grouping, giving (x^3 + x^2) - (16x + 16) = 0. Factoring out the greatest common factor from each pair leaves x^2(x + 1) - 16(x + 1) = 0, which allows us to factor out the binomial (x + 1) to get (x + 1)(x^2 - 16) = 0. Setting each factor to zero provides the solutions x = -1 and x = plus or minus 4.