Question

How do you factor `2x^3+5x^2+2x`?

Answer 1

`f(x) = x(2x^2 + 5x + 2)`
Factor the trinomial in parentheses by the new AC method.

Converted trinomial: f'(x) = 2x^2 + 5x + 4 = (x - p')(x - q')

Product ac = 4. Sum (1 + 4) = 5.= b. The numbers are: p' = 1 and q' = 4.

Then, `p = (p')/a = 1/2`, and `q = (q')/a = 4/2 = 2`

`f(x) = x(x + 1/2)(x + 2) = x(2x + 1)(x + 2)`

Check by developing.
`f(x) = x(2x^2 + 4x + x + 2) = x(2x^2 + 5x + 2).` OK