Question

Which of the following options correctly factorizes the polynomial 504x²+20x-105 completely?

A. 51347−3)(8+7)
B. 5x²(x−3)(x+7)
C. 5x²(x+3)(1−7)
D. 503(x+3)(x−7)

Answer 1

B. 5x²(x−3)(x+7). The correct option for factoring the polynomial 504x²+20x-105 completely is option B. 5x²(x-3)(x+7).

Step-by-step explanation:

The correct option for factoring the polynomial 504x²+20x-105 completely is option B. 5x²(x-3)(x+7).

To factorize the polynomial completely, we need to find the factors of 504, which are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504.

By trial and error, we can determine that combining the factors as 5x²(x-3)(x+7) gives us the original polynomial.