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 $(-7)\times3=-21$ and $-7 + 3=-4$.

Step2: Rewrite the middle - term

Rewrite $x^{2}-4x - 21$ as $x^{2}-7x+3x - 21$.

Step3: Group the terms

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

Step4: Factor out the GCF from each group

Factor out $x$ from the first group and 3 from the second group: $x(x - 7)+3(x - 7)$.

Step5: Factor out the common binomial factor

Factor out $(x - 7)$: $(x - 7)(x+3)$.

Answer:

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