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

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

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Math Problems

Grade 8

Powers with negative bases

Full solution

Q. Factor completely.

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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. $\newline$ $7x^3(x^2 - 3x + 2) = 7x^3(x - 1)(x - 2)$