Questions: One of the factors of 3p^5 - 12p^3 is - p^4 - p+2 - p^2+4 - 4 Question 4(Multiple Choice Worth 1 points) (02.01 MC) Factor completely 50a^2b^5 - 35a^4b^3 + 5a^3b^4. - 5a^2b^3(10b^2 - 7a^2 + ab) - 10b^2 - 7a^2 + ab - a^2b^3(50b^2 - 35a^2 + 5ab) - 5(10a^2b^5 - 7a^4b^3 + a^3b^4)

One of the factors of 3p^5 - 12p^3 is - p^4 - p+2 - p^2+4 - 4 Question 4(Multiple Choice Worth 1 points) (02.01 MC) Factor completely 50a^2b^5 - 35a^4b^3 + 5a^3b^4. - 5a^2b^3(10b^2 - 7a^2 + ab) - 10b^2 - 7a^2 + ab - a^2b^3(50b^2 - 35a^2 + 5ab) - 5(10a^2b^5 - 7a^4b^3 + a^3b^4)
Transcript text: One of the factors of $3 p^{5}-12 p^{3}$ is $p^{4}$ $p+2$ $p^{2}+4$ 4 Question 4(Multiple Choice Worth 1 points) (02.01 MC) Factor completely $50 a^{2} b^{5}-35 a^{4} b^{3}+5 a^{3} b^{4}$. $5 a^{2} b^{3}\left(10 b^{2}-7 a^{2}+a b\right)$ $10 b^{2}-7 a^{2}+a b$ $a^{2} b^{3}\left(50 b^{2}-35 a^{2}+5 a b\right)$ $5\left(10 a^{2} b^{5}-7 a^{4} b^{3}+a^{3} b^{4}\right)$ Previous Question
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Solution

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Solution Steps

To solve the first question, we need to factor the expression \(3p^5 - 12p^3\). We can start by identifying the greatest common factor (GCF) of the terms, which is \(3p^3\). Factoring out the GCF will help us determine the other factor.

For the second question, we need to factor the expression \(50a^2b^5 - 35a^4b^3 + 5a^3b^4\) completely. We should first find the GCF of all the terms, which is \(5a^2b^3\), and then factor it out to simplify the expression.

Step 1: Factor the Expression \(3p^5 - 12p^3\)

To factor the expression \(3p^5 - 12p^3\), we first identify the greatest common factor (GCF) of the terms, which is \(3p^3\). Factoring out the GCF, we have:

\[ 3p^5 - 12p^3 = 3p^3(p^2 - 4) \]

The expression \(p^2 - 4\) is a difference of squares, which can be further factored as:

\[ p^2 - 4 = (p - 2)(p + 2) \]

Thus, the completely factored form of the expression is:

\[ 3p^5 - 12p^3 = 3p^3(p - 2)(p + 2) \]

Step 2: Factor the Expression \(50a^2b^5 - 35a^4b^3 + 5a^3b^4\)

For the expression \(50a^2b^5 - 35a^4b^3 + 5a^3b^4\), we first find the GCF of all the terms, which is \(5a^2b^3\). Factoring out the GCF, we have:

\[ 50a^2b^5 - 35a^4b^3 + 5a^3b^4 = 5a^2b^3(10b^2 - 7a^2 + ab) \]

Thus, the completely factored form of the expression is:

\[ 50a^2b^5 - 35a^4b^3 + 5a^3b^4 = 5a^2b^3(10b^2 - 7a^2 + ab) \]

Final Answer

For the first question, the factorization of \(3p^5 - 12p^3\) is:

\[ \boxed{3p^3(p - 2)(p + 2)} \]

For the second question, the factorization of \(50a^2b^5 - 35a^4b^3 + 5a^3b^4\) is:

\[ \boxed{5a^2b^3(10b^2 - 7a^2 + ab)} \]

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