Question

Check Factor completely. (x²-14)²-8(x²-14)-20 Simplify your answer as much as possible.

Answer 1

To factor the expression (x²-14)²-8(x²-14)-20, let y = (x²-14) and rewrite it as y²-8y-20. Factoring the quadratic equation, we get (y-10)(y+2). Substituting back y = (x²-14), we get (x²-24)(x²-12) as the completely factored expression.

Step-by-step explanation:

To factor the expression
`(x²-14)²-8(x²-14)-20` the expression (x²-14) is repeated twice. We can let y = (x²-14) and rewrite the expression as y²-8y-20. Now, we can factor this quadratic equation to find the factors of (x²-14)²-8(x²-14)-20. Factoring the quadratic equation, we get (y-10)(y+2). Substituting back y = (x²-14), we get the factored expression as ((x²-14)-10)((x²-14)+2), which simplifies to (x²-24)(x²-12). Therefore, the expression is factored completely as (x²-24)(x²-12).