Respuesta :
Answer:
(a) x+3
(b) [tex]x^2+3x+9[/tex]
(c) [tex](x+3)(x^2+9)[/tex]
Step-by-step explanation:
We have given that
(a) [tex]\frac{x^2-9}{x-3}[/tex]
From the algebraic identity we know that
[tex]a^2-b^2=(a+b)(a-b)[/tex]
So [tex]\frac{x^2-9}{x-3}=\frac{(x+3)(x-3)}{x-3}=x+3[/tex]
(b) [tex]\frac{x^3-27}{x-3}[/tex]
We know the algebraic identity
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]
So [tex]\frac{x^3-27}{x-3}=\frac{x^3-3^3}{x-3}=\frac{(x-3)(x^2+3x+9)}{x-3}=x^2+3x+9[/tex]
(c) We have given [tex]\frac{x^4-81}{x-3}[/tex]
We know the algebraic identity
[tex]a^2-b^2=(a+b)(a-b)[/tex]
[tex]\frac{x^4-81}{x-3}=\frac{(x^2)^2-(3^2)^2}{x-3}=\frac{(x^2-9)(x^2+9)}{x-3}=\frac{(x+3)(x-3)(x^2+9)}{x-3}=(x+3)(x^2+9)[/tex]
