90.0k views
3 votes
How to factor x^2 - 3x - 4 (using AC method)? Write steps please.

User Roy Falk
by
8.3k points

1 Answer

1 vote

Final answer:

To factor the quadratic equation x^2 - 3x - 4, we find numbers that multiply to -4 (ac) and add to -3 (b), which are -4 and +1. We then rewrite the middle term, group common factors, and factor out the common binomial, resulting in (x - 4)(x + 1).

Step-by-step explanation:

To factor the quadratic equation x^2 - 3x - 4 using the AC Method, you need to express this equation in the form ax^2 + bx + c = 0, where a, b, and c are integers, and then find two numbers that multiply to ac (the coefficient of x^2 times the constant term) and add up to b (the coefficient of x). The equation x^2 - 3x - 4 has a = 1, b = -3, and c = -4, so ac = -4 and we are looking for two numbers that multiply to -4 and add to -3.

The two numbers that meet these criteria are -4 and +1 because (-4) * (+1) = -4 and (-4) + (+1) = -3. Now we can rewrite the middle term (bx) using these two numbers: x^2 - 4x + x - 4. Next we group the terms: (x^2 - 4x) + (x - 4), and factor by grouping.

The first group has a common factor of x: x(x - 4), and the second group's common factor is +1: +1(x - 4). Now, both groups have a common binomial factor of (x - 4), so we factor this out, resulting in (x - 4)(x + 1).

Hence, the factored form of the equation x^2 - 3x - 4 is (x - 4)(x + 1), which can also be checked by foiling the binomials to see that they equal the original equation.

User Anil Jagtap
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories