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Factor completely $7x^5-21x^4+14x^3=$

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Factor polynomials

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Q. Factor completely

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

Identify GCF: Identify the greatest common factor (GCF) of the terms. $\newline$ The terms are $7x^5$ , $-21x^4$ , and $14x^3$ . $\newline$ The GCF of the coefficients $(7, -21, 14)$ is $7$ . $\newline$ The GCF of the powers of $x$ ( $x^5$ , $x^4$ , $x^3$ ) is $x^3$ . $\newline$ So, the GCF of the entire expression is $-21x^4$ $0$ .
Factor out GCF: Factor out the GCF from each term. $\newline$ $7x^5 - 21x^4 + 14x^3 = 7x^3(x^2 - 3x + 2)$
Factor quadratic: Factor the quadratic expression inside the parentheses. $\newline$ We need to find two numbers that multiply to $2$ (the constant term) and add up to $-3$ (the coefficient of the $x$ term). $\newline$ The numbers that satisfy these conditions are $-1$ and $-2$ . $\newline$ So, the quadratic $x^2 - 3x + 2$ can be factored as $(x - 1)(x - 2)$ .
Write final form: Write the final factored form by combining the GCF and the factored quadratic. $\newline$ $7x^3(x^2 - 3x + 2) = 7x^3(x - 1)(x - 2)$

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