Question

Find the following quotients, and write the quotient in standard form. (a)- x^2-9 ÷ x-3 (b)- x^3-27 ÷ x-3 (c) x^4- 81 ÷ x-3

Answer 1

Answer:

(a) x+3

(b) $x^2+3x+9$

(c) $(x+3)(x^2+9)$

Step-by-step explanation:

We have given that

(a) $\frac{x^2-9}{x-3}$

From the algebraic identity we know that

$a^2-b^2=(a+b)(a-b)$

So $\frac{x^2-9}{x-3}=\frac{(x+3)(x-3)}{x-3}=x+3$

(b) $\frac{x^3-27}{x-3}$

We know the algebraic identity

$a^3-b^3=(a-b)(a^2+ab+b^2)$

So $\frac{x^3-27}{x-3}=\frac{x^3-3^3}{x-3}=\frac{(x-3)(x^2+3x+9)}{x-3}=x^2+3x+9$

(c) We have given $\frac{x^4-81}{x-3}$

We know the algebraic identity

$a^2-b^2=(a+b)(a-b)$

$\frac{x^4-81}{x-3}=\frac{(x^2)^2-(3^2)^2}{x-3}=\frac{(x^2-9)(x^2+9)}{x-3}=\frac{(x+3)(x-3)(x^2+9)}{x-3}=(x+3)(x^2+9)$