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

1 Answer
Jul 24, 2015

Answer:

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)#