Question

Which of the following is the factored form of the expression x²b²-xb²-6b²?

A. b²(x-3)(x+2)
B. b²(x+3)(x-2)
C. b²(x+3)(x+2)
D. b²(x-3)(x-2)

Answer 1

The factored form of the expression is b²(x-3)(x+2), corresponding to option A, after extracting the common factor b² and factoring the quadratic.

Step-by-step explanation:

The factored form of the expression x²b²-xb²-6b² is sought. Factoring out the common factor b² from each term, we get b²(x² - x - 6). We can then factor the quadratic expression in parentheses by finding two numbers that multiply to -6 and add to -1. These numbers are -3 and +2. Therefore, the fully factored form of the expression is b²(x-3)(x+2), which corresponds to option A.