Question

How do you factor completely: `2x^7+10x^5-28x^3`?

Answer 1

Factor: `2x^7 + 10x^5 - 28x^3`

Explanation:

`f(x) = 2x^3(x^4 + 5x - 14). Cal X = x^2`
`f(x) = 2x^3 (X^2 + 5X - 14).`
Factor the quadratic expression f(X) in the parentheses.
Find 2 numbers knowing sum (5) and product (-14).
They are: -2 and 5.
`f(X) = (X - 2)(X + 5) = (x^2 - 2)(x^2 + 5) = (x - sqrt2)(x + sqrt2)(x^2 + 5)`
Finally,
`f(x) = 2x^3(x - sqrt2)(x + sqrt2)(x^2 + 5)`