Question

Khalid carried water bottles to the field to share with his team at halftime. The water bottles weighed a total of 50x² + 30x + 10 ounces Which factorization could represent the number of water bottles and weight of each water bottle?

A 5 (10x² + 15x + 2)
B 2 (25x²-15x + 5)
C (5x + 2) (10x + 5)
D 10 (5x² + 3x + 1)

Answer 1

To factorize the polynomial 50x² + 30x + 10, we must find the greatest common factor, which is 10. The correct factorization is thus 10(5x² + 3x + 1), matching option D from the provided choices.

Step-by-step explanation:

The student is tasked with factorizing a polynomial that represents the total weight of water bottles in ounces. Given the polynomial 50x² + 30x + 10, we seek to factor out the greatest common factor (GCF) from each term. All three terms are divisible by 10, so our factorization will have 10 as the GCF.

Dividing each term by 10, the polynomial becomes 5x² + 3x + 1, which indicates that the correct factorization of the original polynomial is 10(5x² + 3x + 1). This corresponds to option D in the question. Therefore, Khalid may be carrying bottles that each weigh 5x² + 3x + 1 ounces, and there are 10 of these bottles.