Question

1. factor: $x^{2}+x - 20$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to - 20 and add up to 1. The numbers are 5 and - 4 since $5\times(-4)=-20$ and $5+( - 4)=1$.

Step2: Rewrite the middle - term

Rewrite $x^{2}+x - 20$ as $x^{2}+5x-4x - 20$.

Step3: Group the terms

Group the terms: $(x^{2}+5x)-(4x + 20)$.

Step4: Factor out the greatest common factor from each group

Factor out $x$ from the first group and 4 from the second group: $x(x + 5)-4(x + 5)$.

Step5: Factor out the common binomial factor

Factor out $(x + 5)$: $(x + 5)(x-4)$.

Answer:

$(x + 5)(x - 4)$