Question

Compute each quotient. (a) x^2-625 ÷ x-25 (b) x^3+1 ÷ x+1 (c) x^3- ⅛ ÷ x- ½ (d) x^2- 0.01 ÷ x- 0.1

Answer 1

Answer:

(a) $x+25$

(b)  $x^2-x+1$

(c) $(x^2+\frac{x}{2}+\frac{1}{4})$

(d)  x-0.1

Step-by-step explanation:

We have to compute

(a) $\frac{x^2-625}{x-25}$

We know the algebraic equation $a^2-b^2=(a+b)(a-b)$

So $\frac{x^2-625}{x-25}=\frac{x^2-25^2}{x-25}=[tex]x+25$

(b) We have to compute $\frac{x^3+1}{x+1}$

We know the algebraic equation $a^3+b^3=(a+b)(a^2-ab+b^2)$

So $\frac{x^3+1}{x+1}=\frac{(x+1)(x^2-x+1)}{x+1}=x^2-x+1$

(c) We have to compute $\frac{x^3-\frac{1}{8}}{x-\frac{1}{2}}$

We know the algebraic equation  $a^3-b^3=(a-b)(a^2+ab+b^2)$

$\frac{x^3-\frac{1}{8}}{x-\frac{1}{2}}=\frac{(x-\frac{1}{2})(x^2+\frac{x}{2}+\frac{1}{4})}{x-\frac{1}{2}}$

$(x^2+\frac{x}{2}+\frac{1}{4})$

(d) We have to compute $\frac{x^2-0.01}{x+0.1}$

We know the algebraic equation $a^2-b^2=(a+b)(a-b)$

$\frac{x^2-0.01}{x+0.1}=\frac{(x+0.1)(x-0.1)}{x+0.1}=x-0.1$