Question

See ss below
please explain each step ​

Answer 1

p(x) = (x - 5)(x + 1)(x + 4)

General Formulas and Concepts:

Algebra I

• Terms/Coefficients
• Factoring

Algebra II

• Factoring Cubes:
  `\displaystyle (a \pm b)(ax^2 \mp bx + c)`
• Long Division
• Synthetic Division

Explanation:

*Note:

Please excuse my bad handwriting :)

Step 1: Define

Identify

p(x) = x³ - 21x - 20

Linear factor (x - 5)

Step 2: Factor

Option 1: Factoring cubes formula

1. Factor [Factoring Cubes]: p(x) = (x - 5)(x² + 5x + 4)
2. Factor: p(x) = (x - 5)(x + 4)(x + 1)

Option 2: Long Division

See Attachment

Option 3: Synthetic Division

See Attachment #2