Factor completely. 5x^(2)-20 x+20=

Identify common factor: Identify if the quadratic can be factored using common factoring techniques. We are looking to factor the quadratic expression 5x^2 - 20x + 20. We can check if there is a common factor for all terms first. The common factor for all terms is 5.Factor out common factor: Factor out the greatest common factor from the quadratic expression. 5x^2 - 20x + 20 = 5(x^2 - 4x + 4)Check for further factoring: Check if the quadratic expression inside the parentheses can be factored further. The quadratic x^2 - 4x + 4 is a perfect square trinomial because it can be written as (x - 2)^2.Factor perfect square trinomial: Factor the perfect square trinomial. x^2 - 4x + 4 = (x - 2)(x - 2) or (x - 2)^2Write final factored form: Write the final factored form of the original quadratic expression. 5x^2 - 20x + 20 = 5(x - 2)^2

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Math Problems

Algebra 1

Factor quadratics: special cases

Full solution

Q. Factor completely.

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5x^{2}-20x+20=

Identify common factor: Identify if the quadratic can be factored using common factoring techniques. $\newline$ We are looking to factor the quadratic expression $5x^2 - 20x + 20$ . We can check if there is a common factor for all terms first. $\newline$ The common factor for all terms is $5$ .
Factor out common factor: Factor out the greatest common factor from the quadratic expression. $\newline$ $5x^2 - 20x + 20 = 5(x^2 - 4x + 4)$
Check for further factoring: Check if the quadratic expression inside the parentheses can be factored further. $\newline$ The quadratic $x^2 - 4x + 4$ is a perfect square trinomial because it can be written as $(x - 2)^2$ .
Factor perfect square trinomial: Factor the perfect square trinomial. $x^2 - 4x + 4 = (x - 2)(x - 2)$ or $(x - 2)^2$
Write final factored form: Write the final factored form of the original quadratic expression. $\newline$ $5x^2 - 20x + 20 = 5(x - 2)^2$