What is the completely factored form of 3x^5 7x^4 6x^2 14x?

To find the completely factored form of the expression 3x⁵ 7x⁴ 6x² 14x, we first need to factor each coefficient and combine all the terms involving the variable x.

Let’s break it down step by step:

• The coefficients are 3, 7, 6, and 14. We can factor these numbers:
• 3: This is a prime number.
• 7: This is also a prime number.
• 6: This factors to 2 × 3.
• 14: This factors to 2 × 7.
• Combining these gives us the prime factors:
• 3 (from 3 and 6)
• 7 (from 7 and 14)
• 2 (from 6 and 14)
• Next, we look at the x terms:
• x⁵: The highest power in the expression.
• x⁴, x², and x: The other powers present.
• The common factor across the x terms is x, and the least power is x¹.

Now, we can write the combined factors. The coefficients’ common factors are:

• 2 (appears in 6 and 14)
• 3 (appears in 3 and 6)
• 7 (appears in 7 and 14)

So, the factored form of the coefficients is:

2 × 3 × 7 = 42

For the x terms, we take the smallest power, which is:

x¹

Combining everything together, the completely factored form of 3x⁵ 7x⁴ 6x² 14x is:

42x¹

Therefore, the final answer is:

42x