Question 26

(b + 4)(b - 1)

The expression b^2 + 3b - 4 factors completely to (b + 4)(b - 1). This can be verified by expanding the factors to confirm that they yield the original quadratic expression.

A) (b + 4)(b - 1)

This option is correct. When expanded, (b + 4)(b - 1) gives b^2 - b + 4b - 4, which simplifies to b^2 + 3b - 4, matching the original expression.

B) (b - 2)(b - 3)

This option is incorrect. Expanding (b - 2)(b - 3) results in b^2 - 3b + 2b - 6, simplifying to b^2 - b - 6, which does not match the original expression.

C) (b + 1)(b + 2)

This option is also incorrect. Upon expansion, (b + 1)(b + 2) yields b^2 + 2b + 1b + 2, which simplifies to b^2 + 3b + 2, differing from the original quadratic.

D) (b + 3)(b - 1)

This option is incorrect as well. Expanding (b + 3)(b - 1) results in b^2 - b + 3b - 3, which simplifies to b^2 + 2b - 3, not matching the original expression.

Conclusion

The correct answer is (b + 4)(b - 1) as it accurately factors the quadratic expression b^2 + 3b - 4. All other options fail to provide the correct factorization, either resulting in different expressions or not being reducible to the original form. Thus, option A is definitively the accurate choice.