{
  "problem": "Factor completely. $2x^4+4x^3-30x^2=$",
  "hints": [
    "As a first step, let's see if there's a common factor we can factor out.",
    "Greatest common factor The greatest common factor of $2x^4$, $4x^3$, and $-30x^2$ is $2x^2$. Let's factor $2x^2$ out of $2x^4+4x^3-30x^2$ : $\\begin{aligned} &\\phantom{=}2x^4+4x^3-30x^2 \\\\\\\\ &=2x^2(x^2)+2x^2(2x)+2x^2(-15) \\\\\\\\ &=2x^2(x^2+2x-15) \\end{aligned}$ We can keep factoring the expression by factoring $x^2+2x-15$.",
    "Factoring $x^2+2x-15$ $x^2+2x-15=(x+5)(x-3)$",
    "Putting it all together $\\begin{aligned} &\\phantom{=}2x^4+4x^3-30x^2 \\\\\\\\ &=2x^2(x^2+2x-15) \\\\\\\\ &=2x^2(x+5)(x-3) \\end{aligned}$",
    "In conclusion, this is the completely factored expression: $2x^2(x+5)(x-3)$"
  ]
}
{'source': 'AMPS', 'file': 'amps/khan/factor-higher-degree-polynomials/16073363313.json'}