Factor completely: b^2 + 3b - 4

Rationale

(b + 4)(b - 1)

To factor the quadratic expression b² + 3b - 4 completely, we look for two numbers that multiply to -4 (the constant term) and add to 3 (the coefficient of the linear term). The numbers 4 and -1 satisfy these conditions, leading to the factors (b + 4) and (b - 1).

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

This choice represents the correct factorization of the expression b² + 3b - 4. When expanded, (b + 4)(b - 1) results in b² + 3b - 4, confirming that it is indeed the correct answer.

B ((b - 2)(b - 3)) YOUR ANSWER

This choice does not correctly factor the expression. When expanded, (b - 2)(b - 3) results in b² - 5b + 6, which does not match the original expression b² + 3b - 4, indicating that it is incorrect.

C ((b + 1)(b + 2)) YOUR ANSWER

This option is also incorrect as the expansion of (b + 1)(b + 2) yields b² + 3b + 2. The resulting quadratic has a different constant term than the original expression, confirming that this factorization is not valid.

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

This choice is incorrect because expanding (b + 3)(b - 1) gives b² + 2b - 3. The linear and constant coefficients do not match those of the original expression, demonstrating that this is not the correct factorization.

Conclusion

The expression b² + 3b - 4 factors completely into (b + 4)(b - 1), as verified by the conditions for factorization. The other options fail to provide the correct product upon expansion, highlighting the uniqueness of the correct answer. Understanding how to factor quadratics is essential in algebra, enabling simplification and solving of polynomial equations efficiently.

Factor completely: b^2 + 3b - 4

(b + 4)(b - 1)

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test