Question

completely factor the polynomial, if possible.

\\8xy^2 - 40xy + 50x\\

Explanation:

Factor out the greatest common factor

Using the Factoring Polynomials by GCF knowledge point

$$ 8xy^2 - 40xy + 50x = 2x(4y^2 - 20y + 25) $$

Identify the trinomial pattern

Using the Factoring Trinomials and Square of a Binomial Difference knowledge points

$$
LATEXBLOCK0
$$

Factor the perfect square trinomial

Using the Square of a Binomial Difference knowledge point

$$ 4y^2 - 20y + 25 = (2y - 5)^2 $$

Write the completely factored expression

Using the Factoring Polynomials by GCF and Square of a Binomial Difference knowledge points

$$ 8xy^2 - 40xy + 50x = 2x(2y - 5)^2 $$

Answer:

\(2x(2y - 5)^2\)