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

(a)
`x+25`

(b)
`x^2-x+1`

(c)
`(x^2+(x)/(2)+(1)/(4))`

(d) x-0.1

Explanation:

We have to compute

(a)
`(x^2-625)/(x-25)`

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

So
`(x^2-625)/(x-25)=(x^2-25^2)/(x-25)=[tex]x+25`

(b) We have to compute
`(x^3+1)/(x+1)`

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

So
`(x^3+1)/(x+1)=((x+1)(x^2-x+1))/(x+1)=x^2-x+1`

(c) We have to compute
`(x^3-(1)/(8))/(x-(1)/(2))`

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

`(x^3-(1)/(8))/(x-(1)/(2))=((x-(1)/(2))(x^2+(x)/(2)+(1)/(4)))/(x-(1)/(2))`

`(x^2+(x)/(2)+(1)/(4))`

(d) We have to compute
`(x^2-0.01)/(x+0.1)`

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

`(x^2-0.01)/(x+0.1)=((x+0.1)(x-0.1))/(x+0.1)=x-0.1`