Factor completely. 5x^(4)-20x^(3)+20x^(2)=

Identify GCF: Identify the greatest common factor (GCF) of the terms. The GCF of 5x^4, 20x^3, and 20x^2 is 5x^2.Factor out GCF: Factor out the GCF from each term. 5x^4 - 20x^3 + 20x^2 = 5x^2(x^2 - 4x + 4)Recognize quadratic trinomial: Recognize that the expression inside the parentheses is a quadratic trinomial. We need to determine if the quadratic trinomial (x^2 - 4x + 4) can be factored further.Factor quadratic trinomial: Factor the quadratic trinomial. The quadratic trinomial x^2 - 4x + 4 is a perfect square trinomial because (2)^2 = 4 and 2*2 = 4. It factors into (x - 2)^2.Write completely factored form: Write the completely factored form of the original expression. 5x^4 - 20x^3 + 20x^2 = 5x^2(x - 2)^2

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Factor completely.

5x^(4)-20x^(3)+20x^(2)=

Factor completely. $\newline$ $5 x^{4}-20 x^{3}+20 x^{2}=$

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Math Problems

Grade 8

Powers with negative bases

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Q. Factor completely.

\newline

5 x^{4}-20 x^{3}+20 x^{2}=

Identify GCF: Identify the greatest common factor (GCF) of the terms. $\newline$ The GCF of $5x^4$ , $20x^3$ , and $20x^2$ is $5x^2$ .
Factor out GCF: Factor out the GCF from each term. $\newline$ $5x^4 - 20x^3 + 20x^2 = 5x^2(x^2 - 4x + 4)$
Recognize quadratic trinomial: Recognize that the expression inside the parentheses is a quadratic trinomial. We need to determine if the quadratic trinomial $(x^2 - 4x + 4)$ can be factored further.
Factor quadratic trinomial: Factor the quadratic trinomial. $\newline$ The quadratic trinomial $x^2 - 4x + 4$ is a perfect square trinomial because $(2)^2 = 4$ and $2\times2 = 4$ . $\newline$ It factors into $(x - 2)^2$ .
Write completely factored form: Write the completely factored form of the original expression. $\newline$ $5x^4 - 20x^3 + 20x^2 = 5x^2(x - 2)^2$