Question

17 multiple choice 6 points solve the equation. \\( x^3 + 3x^2 + 49x + 147 = 0 \\) \\( \\{ -3, -7i, 7i \\} \\) \\( \\{ -sqrt{3}, sqrt{3}, 7i \\} \\) \\( \\{ -3, -sqrt{7}, sqrt{7} \\} \\) \\( \\{ -3, 49i, 7i \\} \\) clear my selection

Explanation:

Step1: Factor by grouping

Group the terms: \((x^3 + 3x^2) + (49x + 147) = 0\)
Factor out common terms: \(x^2(x + 3) + 49(x + 3) = 0\)
Factor out \((x + 3)\): \((x + 3)(x^2 + 49) = 0\)

Step2: Solve for \(x\)

Set each factor equal to zero:

1. \(x + 3 = 0 \implies x = -3\)
2. \(x^2 + 49 = 0 \implies x^2 = -49 \implies x = \pm 7i\)

Answer:

\(\{-3, -7i, 7i\}\) (the first option: \(\{-3, -7i, 7i\}\))