what is the factored form of $x^{2}-x - 2$?\n$(x - 2)(x + 1)$\n$(x + 2)(x + 1)$\n$(x - 2)(x - 1)$\n$(x +…
what is the factored form of $x^{2}-x - 2$?\n$(x - 2)(x + 1)$\n$(x + 2)(x + 1)$\n$(x - 2)(x - 1)$\n$(x + 2)(x - 1)$
Answer
Answer:
A. $(x - 2)(x + 1)$
Explanation:
Step1: Identify coefficients
For $x^{2}-x - 2$, $a = 1$, $b=-1$, $c=-2$.
Step2: Find two numbers
We need two numbers that multiply to $ac=1\times(-2)= - 2$ and add up to $b=-1$. The numbers are $-2$ and $1$ since $(-2)\times1=-2$ and $-2 + 1=-1$.
Step3: Rewrite middle - term
Rewrite $x^{2}-x - 2$ as $x^{2}-2x+x - 2$.
Step4: Group terms
Group the terms: $(x^{2}-2x)+(x - 2)$.
Step5: Factor out GCF from each group
Factor out the GCF from each group: $x(x - 2)+1(x - 2)$.
Step6: Factor out common binomial
Factor out the common binomial $(x - 2)$ to get $(x - 2)(x + 1)$.