question\nfactor.\n$x^{2}+4x - 21$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to - 21 and add up to 4. The numbers are 7 and - 3 since (7\times(-3)=-21) and (7+( - 3)=4).

Step2: Rewrite the middle - term

Rewrite the quadratic expression (x^{2}+4x - 21) as (x^{2}+7x-3x - 21).

Step3: Group the terms

Group the terms: ((x^{2}+7x)+(-3x - 21)).

Step4: Factor out the greatest common factor from each group

From the first group (x^{2}+7x), the GCF is (x), so we get (x(x + 7)). From the second group (-3x - 21), the GCF is - 3, so we get (-3(x + 7)).

Step5: Factor out the common binomial factor

We have (x(x + 7)-3(x + 7)=(x + 7)(x - 3)).

Answer:

((x + 7)(x - 3))