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

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

Answer

Explanation:

Step1: Recall division - multiplication relationship

We know that if (a\div b = c), then (b\times c=a). Here (a = x^{2}-4), (b=x + 2) and (c) is the unknown polynomial. Given ((x^{2}-4)\div(x + 2)=x - 2), we can rewrite it in multiplication form.

Step2: Apply the relationship

Since ((x^{2}-4)\div(x + 2)=x - 2), then ((x + 2)\times(x - 2)=x^{2}-4) (using the difference - of - squares formula ((a + b)(a - b)=a^{2}-b^{2}), where (a=x) and (b = 2)). So the polynomial that should fill in the blank is (x - 2).

Answer:

B. (x - 2)