{
"query": {
"display": "factor $$x^{2}-x-20$$",
"symbolab_question": "FACTOR#factor x^{2}-x-20"
},
"solution": {
"level": "PERFORMED",
"subject": "Algebra",
"topic": "Algebra",
"subTopic": "Simplify",
"default": "(x+4)(x-5)",
"meta": {
"showVerify": true
}
},
"steps": {
"type": "interim",
"title": "Factorizar $$x^{2}-x-20:{\\quad}\\left(x+4\\right)\\left(x-5\\right)$$",
"input": "x^{2}-x-20",
"steps": [
{
"type": "interim",
"title": "Factorizar la expresión",
"input": "x^{2}-x-20",
"steps": [
{
"type": "definition",
"title": "Definición",
"text": "Para $$ax^{2}+bx+c\\:$$encontrar $$u,\\:v\\:$$ tal que: $$u\\cdot\\:v=a\\cdot\\:c\\:$$y $$u+v=b$$<br/>Después agrupar de acuerdo a $$\\left(ax^{2}+ux\\right)+\\left(vx+c\\right)$$",
"secondary": [
"$$a=1,\\:b=-1,\\:c=-20$$",
"$$u*v=-20,\\:u+v=-1$$"
]
},
{
"type": "interim",
"title": "Factores de $$20:{\\quad}1,\\:2,\\:4,\\:5,\\:10,\\:20$$",
"input": "20",
"steps": [
{
"type": "definition",
"title": "Divisores (factores)",
"text": "Un número que divide a un entero sin dejar residuo"
},
{
"type": "interim",
"title": "Encontrar los factores primos de $$20:{\\quad}2,\\:2,\\:5$$",
"input": "20",
"steps": [
{
"type": "step",
"primary": "$$20\\:$$divida por $$2\\quad\\:20=10\\cdot\\:2$$",
"result": "=2\\cdot\\:10"
},
{
"type": "step",
"primary": "$$10\\:$$divida por $$2\\quad\\:10=5\\cdot\\:2$$",
"result": "=2\\cdot\\:2\\cdot\\:5"
},
{
"type": "step",
"primary": "$$2,\\:5$$ son números primos, por lo tanto, no se pueden factorizar mas",
"result": "=2\\cdot\\:2\\cdot\\:5"
}
],
"meta": {
"interimType": "Find The Prime Factors Of Title 1Eq",
"gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3PHQdChPJ2JhfqHT+ZU0OMrfn8NOj0LUzuzje6xTyxRpfAIYH0B5pAUto4RYxQ3UuBBTEk/JQ2cZ9WKuRzClU7UwjtyZ+HZsnJSINeAcpXDfm50zKC+6CoqeDw0ARlmJ6922Vhe1JaYRuC1bNj8we0"
}
},
{
"type": "interim",
"title": "Multiplicar los factores primos de $$20:{\\quad}4,\\:10$$",
"result": "4,\\:10",
"steps": [
{
"type": "step",
"primary": "$$2\\cdot\\:2=4$$",
"secondary": [
"$$2\\cdot\\:5=10$$"
]
},
{
"type": "step",
"result": "4,\\:10"
}
],
"meta": {
"interimType": "Multiply the prime factors 1Eq"
}
},
{
"type": "step",
"primary": "Agregar factores primos:",
"result": "2,\\:5"
},
{
"type": "step",
"primary": "Agregar 1 y su propio número $$20$$",
"result": "1,\\:20"
},
{
"type": "step",
"primary": "Divisores de $$20$$",
"result": "1,\\:2,\\:4,\\:5,\\:10,\\:20"
}
],
"meta": {
"solvingClass": "Composite Integer",
"interimType": "Factors Top 1Eq"
}
},
{
"type": "interim",
"title": "Factores negativos de $$20:{\\quad}-1,\\:-2,\\:-4,\\:-5,\\:-10,\\:-20$$",
"steps": [
{
"type": "step",
"primary": "Multiplicar los números por $$-1$$ para obtener divisores negativos",
"result": "-1,\\:-2,\\:-4,\\:-5,\\:-10,\\:-20"
}
],
"meta": {
"interimType": "Negative Factors Top 1Eq"
}
},
{
"type": "interim",
"title": "Por cada dos factores tales que $$u*v=-20,\\:$$revisar si $$u+v=-1$$",
"steps": [
{
"type": "step",
"primary": "Revisar $$u=1,\\:v=-20:\\quad\\:u*v=-20,\\:u+v=-19\\quad\\Rightarrow\\quad\\:$$Falso",
"secondary": [
"Revisar $$u=2,\\:v=-10:\\quad\\:u*v=-20,\\:u+v=-8\\quad\\Rightarrow\\quad\\:$$Falso",
"Revisar $$u=4,\\:v=-5:\\quad\\:u*v=-20,\\:u+v=-1\\quad\\Rightarrow\\quad\\:$$Verdadero",
"Revisar $$u=5,\\:v=-4:\\quad\\:u*v=-20,\\:u+v=1\\quad\\Rightarrow\\quad\\:$$Falso",
"Revisar $$u=10,\\:v=-2:\\quad\\:u*v=-20,\\:u+v=8\\quad\\Rightarrow\\quad\\:$$Falso",
"Revisar $$u=20,\\:v=-1:\\quad\\:u*v=-20,\\:u+v=19\\quad\\Rightarrow\\quad\\:$$Falso"
]
}
],
"meta": {
"interimType": "Factor Break Into Groups Check UV Combinations 2Eq"
}
},
{
"type": "step",
"result": "u=4,\\:v=-5"
},
{
"type": "step",
"primary": "Agrupar en $$\\left(ax^{2}+ux\\right)+\\left(vx+c\\right)$$",
"result": "\\left(x^{2}+4x\\right)+\\left(-5x-20\\right)"
}
],
"meta": {
"interimType": "Factor Break Into Groups 0Eq",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7mbLwQunn5/3JzwqIhKjMwiTAtHwe77KW105uEUM7Z4osjvX7KVUO/AeCFSId4S337bTjH0JhPfEDoyROh2MmxOR81aIMFSjUznRIvxWbLKE8+48ptyTmxmUSr1Die6IXWkk+Kt1eMHZLTaqpS1jGzXZhM8lCwnFCbTYyb00yC/lPiU9GJuZxnqYltPC06V2rxzxSLzprhwTbfkufQcmC8A=="
}
},
{
"type": "step",
"result": "=\\left(x^{2}+4x\\right)+\\left(-5x-20\\right)"
},
{
"type": "interim",
"title": "Factorizar $$x$$ de $$x^{2}+4x$$:$${\\quad}x\\left(x+4\\right)$$",
"input": "x^{2}+4x",
"steps": [
{
"type": "step",
"primary": "Aplicar las leyes de los exponentes: $$a^{b+c}=a^{b}a^{c}$$",
"secondary": [
"$$x^{2}=xx$$"
],
"result": "=xx+4x",
"meta": {
"practiceLink": "/practice/exponent-practice",
"practiceTopic": "Expand FOIL"
}
},
{
"type": "step",
"primary": "Factorizar el termino común $$x$$",
"result": "=x\\left(x+4\\right)",
"meta": {
"practiceLink": "/practice/factoring-practice",
"practiceTopic": "Factoring"
}
}
],
"meta": {
"interimType": "Factor Out Specific 3Eq",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7fyAweyQvVwJsSQQKDjm97PUMABIQKMSMaYSzBXqqWZF1C4k27jzuj6KLnWyn2hb8bFwMwSf2fjKgNqIbLArbNOLWXfeXo8KExseWXOwkmyd24affICWdjh78fVRVNyyCbUPECyN5wz29EsDeaqJzOTKH6+6Rjrttm82D0zaTG7NhiXhm+tWmf81LCyHr11dG"
}
},
{
"type": "interim",
"title": "Factorizar $$-5$$ de $$-5x-20$$:$${\\quad}-5\\left(x+4\\right)$$",
"input": "-5x-20",
"steps": [
{
"type": "step",
"primary": "Reescribir $$-20$$ como $$-5\\cdot\\:4$$",
"result": "=-5x-5\\cdot\\:4"
},
{
"type": "step",
"primary": "Factorizar el termino común $$-5$$",
"result": "=-5\\left(x+4\\right)",
"meta": {
"practiceLink": "/practice/factoring-practice",
"practiceTopic": "Factoring"
}
}
],
"meta": {
"interimType": "Factor Out Specific 3Eq",
"gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7azZp4DB+B1N0dq43DKjaOxyOUtErWNRXbTqqjj69E3uBgn/GSIMdAWH6UHJYQzHa0KOEq32rRoLFZaty3uWqn0V5htgN+qCwR6RjLiy0n4bMPF9tfONRiFlp3oxDMg6V0VeniH18fdvVdYaXIYkayDTAy4e1bvJbkvbeuPbaF8nthAt+KtnhoBG7AiLI4ujK"
}
},
{
"type": "step",
"result": "=x\\left(x+4\\right)-5\\left(x+4\\right)"
},
{
"type": "step",
"primary": "Factorizar el termino común $$x+4$$",
"result": "=\\left(x+4\\right)\\left(x-5\\right)",
"meta": {
"practiceLink": "/practice/factoring-practice",
"practiceTopic": "Factoring"
}
}
],
"meta": {
"solvingClass": "Solver2"
}
},
"meta": {
"showVerify": true
}
}
Solución
factor
Solución
Pasos de solución
Factorizar la expresión
Factorizar de :
Factorizar de :
Factorizar el termino común