Question

Write in Factored Form: x² + 3x - 28

Show all of your work including Factors of AC and Sum of B.

Answer 1

The quadratic equation x² + 3x - 28 can be factored into (x + 7)(x - 4) by finding two numbers that multiply to -28 and add to 3.

Step-by-step explanation:

The equation x² + 3x - 28 is a quadratic equation and can be factored by finding two numbers that multiply to give the product (AC) of the leading coefficient and the constant term (-28) and add to give the middle coefficient (B) of 3.

In this case, the two numbers that satisfy this condition are 7 and -4. The factored form of the quadratic equation is (x + 7)(x - 4).

Here's the step-by-step process:

1. Identify the coefficients and constant in the quadratic equation: A=1, B=3, C=-28.
2. Find two numbers that multiply to give AC (-28) and add up to B (3): the numbers are 7 and -4, because 7*(-4) = -28 and 7+(-4) = 3.
3. Write the original quadratic in the form of x² + 7x - 4x - 28, grouping the terms as (x² + 7x) + (-4x - 28).
4. Factor by grouping: x(x + 7) - 4(x + 7).
5. Factor out the common binomial: (x + 7)(x - 4).