if $(x^{2}-4)div(x + 2)=x - 2$, which polynomial should fill in the blank below?\n$(x + 2)\times\\underline{\…

if $(x^{2}-4)div(x + 2)=x - 2$, which polynomial should fill in the blank below?\n$(x + 2)\times\\underline{\\quad\\quad}=x^{2}-4$\n$\\bigcirc x^{2}-4$\n$\\bigcirc x - 2$\n$\\bigcirc x + 2$\n$\\bigcirc x^{2}-2$

if $(x^{2}-4)div(x + 2)=x - 2$, which polynomial should fill in the blank below?\n$(x + 2)\times\\underline{\\quad\\quad}=x^{2}-4$\n$\\bigcirc x^{2}-4$\n$\\bigcirc x - 2$\n$\\bigcirc x + 2$\n$\\bigcirc x^{2}-2$

Answer

Answer:

B. $x - 2$

Explanation:

Step1: Recall division - multiplication relationship

If $a\div b = c$, then $b\times c=a$. Here $a=x^{2}-4$, $b = x + 2$ and $c=x - 2$.

Step2: Identify the missing polynomial

Given $(x^{2}-4)\div(x + 2)=x - 2$, then $(x + 2)\times(x - 2)=x^{2}-4$ according to the division - multiplication inverse relationship. So the polynomial to fill in the blank is $x - 2$.