Factor completely: 6p^(2)-7pa^(5)-3a^(10) Answer:

Identify GCF: Identify the greatest common factor (GCF) of the terms in the polynomial 6p^2 - 7pa^5 - 3a^10. The GCF of 6p^2, -7pa^5, and -3a^10 is a^5, since it is the highest power of a that divides each term.Factor out GCF: Factor out the GCF from each term in the polynomial. 6p^2 - 7pa^5 - 3a^10 = a^5(6p^2/a^5 - 7p - 3a^5/a^5) Simplify the terms inside the parentheses. 6p^2/a^5 = 6p^2 * a^(-5) = 6/a^3 * p^2 -3a^10/a^5 = -3a^(10-5) = -3a^5 So, the factored form is a^5(6/a^3 * p^2 - 7p - 3a^5).Correct factoring: Notice that the term 6/a^3 * p^2 is not a polynomial term, which indicates a mistake was made in the previous step. We need to correct this. The correct factoring of the GCF is: 6p^2 - 7pa^5 - 3a^10 = a^5(6p^2/a^5 - 7p/a^5 - 3a^10/a^5) Simplify the terms inside the parentheses. 6p^2/a^5 = 6p^2 * a^(-5) = 6p^2/a^5 -7pa^5/a^5 = -7p -3a^10/a^5 = -3a^(10-5) = -3a^5 So, the corrected factored form is a^5(6p^2/a^5 - 7p - 3a^5).

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Factor completely:

6p^(2)-7pa^(5)-3a^(10)
Answer:

Factor completely: $\newline$ $6 p^{2}-7 p a^{5}-3 a^{10}$ $\newline$ Answer:

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Q. Factor completely:

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6 p^{2}-7 p a^{5}-3 a^{10}

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Answer:

Identify GCF: Identify the greatest common factor (GCF) of the terms in the polynomial $6p^2 - 7pa^5 - 3a^{10}$ . The GCF of $6p^2$ , $-7pa^5$ , and $-3a^{10}$ is $a^5$ , since it is the highest power of $a$ that divides each term.
Factor out GCF: Factor out the GCF from each term in the polynomial. $\newline$ $6p^2 - 7pa^5 - 3a^{10} = a^5(\frac{6p^2}{a^5} - 7p - \frac{3a^{10}}{a^5})$ $\newline$ Simplify the terms inside the parentheses. $\newline$ $\frac{6p^2}{a^5} = 6p^2 \cdot a^{-5} = \frac{6}{a^3} \cdot p^2$ $\newline$ $-\frac{3a^{10}}{a^5} = -3a^{10-5} = -3a^5$ $\newline$ So, the factored form is $a^5(\frac{6}{a^3} \cdot p^2 - 7p - 3a^5)$ .
Correct factoring: Notice that the term $\frac{6}{a^3} \cdot p^2$ is not a polynomial term, which indicates a mistake was made in the previous step. We need to correct this. $\newline$ The correct factoring of the GCF is: $\newline$ $6p^2 - 7pa^5 - 3a^{10} = a^5\left(\frac{6p^2}{a^5} - \frac{7p}{a^5} - \frac{3a^{10}}{a^5}\right)$ $\newline$ Simplify the terms inside the parentheses. $\newline$ $\frac{6p^2}{a^5} = 6p^2 \cdot a^{-5} = \frac{6p^2}{a^5}$ $\newline$ $\frac{-7pa^5}{a^5} = -7p$ $\newline$ $\frac{-3a^{10}}{a^5} = -3a^{10-5} = -3a^5$ $\newline$ So, the corrected factored form is $a^5\left(\frac{6p^2}{a^5} - 7p - 3a^5\right)$ .