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Factor completely.

7x^(5)-21x^(4)+14x^(3)=

Factor completely. $\newline$ $7 x^{5}-21 x^{4}+14 x^{3}=$

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Powers with negative bases

Full solution

Q. Factor completely.

\newline

7 x^{5}-21 x^{4}+14 x^{3}=

Identify GCF of terms: Identify the greatest common factor (GCF) of the terms. $\newline$ The terms $7x^5$ , $-21x^4$ , and $14x^3$ all have a common factor of $7x^3$ . $\newline$ GCF: $7x^3$
Factor out GCF from each term: Factor out the GCF from each term. $\newline$ Factor $7x^3$ out of each term to simplify the polynomial. $\newline$ $7x^5 - 21x^4 + 14x^3 = 7x^3(x^2 - 3x + 2)$
Factor quadratic expression: Factor the quadratic expression within the parentheses. $\newline$ The quadratic $x^2 - 3x + 2$ can be factored further since it is a simple trinomial. $\newline$ Factors of $2$ that add up to $-3$ are $-1$ and $-2$ . $\newline$ $x^2 - 3x + 2 = (x - 1)(x - 2)$
Write completely factored form: Write the completely factored form of the original polynomial. $\newline$ Combine the GCF with the factored form of the quadratic. $\newline$ $7x^3(x^2 - 3x + 2) = 7x^3(x - 1)(x - 2)$

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1 . \overline{3}

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