question\nfactor.\n$x^{2}-x - 20$

Answer

Explanation:

Step1: Identify coefficient and constant

For the quadratic expression $x^{2}-x - 20$, the coefficient of $x^{2}$ is 1, the coefficient of $x$ is - 1, and the constant is -20.

Step2: Find two numbers

We need two numbers that multiply to $1\times(-20)=-20$ and add up to -1. The numbers are -5 and 4 since $(-5)\times4=-20$ and $-5 + 4=-1$.

Step3: Rewrite the middle - term

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

Step4: Group the terms

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

Step5: Factor out the GCF from each group

Factor out the greatest - common factor (GCF) from each group. From $x^{2}-5x$, the GCF is $x$, so $x^{2}-5x=x(x - 5)$. From $4x - 20$, the GCF is 4, so $4x - 20=4(x - 5)$.

Step6: Factor out the common binomial factor

We have $x(x - 5)+4(x - 5)=(x - 5)(x + 4)$.

Answer:

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