Question

Match the rational expressions to their quotients

Answer 1

Given rational expressions:

1.
`(x^+13x+54)/(x+6)`

2.
`(x^+3x-23)/(x+6)`

3.
`(x^+9x+20)/(x+7)`

4.
`(x^+5x-20)/(x+7)`

To match with given Quotients.

Quotients are x + 7 , x - 3 , x + 2 and x - 2

We Divide given expression using long division of the polynomilas.

All divisions done in pics.

1. On Dividing we get,

Quotient = x + 7 and Remainder = 12

2. On Dividing we get,

Quotient = x - 3 and Remainder = -5

3. On Dividing we get,

Quotient = x + 2 and Remainder = 6

4. On Dividing we get,

Quotient = x - 2 and Remainder = -6

Therefore,

Quotient Expressions

`\:\:\:x+2----------\rightarrow(x^+9x+20)/(x+7)`

`\:\:\:x-3----------\rightarrow(x^+3x-23)/(x+6)`

`\:\:\:x-2----------\rightarrow(x^+5x-20)/(x+7)`

`\:\:\:x+7----------\rightarrow(x^+13x+54)/(x+6)`

Answer 2

The quotient (x + 2) ⇒ the expression
`(x^(2)+9x+20 )/(x+7)`

The quotient (x - 3) ⇒ the expression
`(x^(2)+3x-23 )/(x+6)`

The quotient (x - 2) ⇒ the expression
`(x^(2)+5x-20 )/(x+7)`

The quotient (x + 7) ⇒ the expression
`(x^(2)+13x+54 )/(x+6)`

Explanation:

∵
`(x^(2)+9x+20 )/(x+7)=x+(2x+20)/(x+7)`

∵
`(2x+20)/(x+7)= 2+(6)/(x+7)`

∴ The quotient is x + 2

∵
`(x^(2)+3x-23 )/(x+6)=x+(-3x-23)/(x+6)`

∵
`(-3x-23)/(x+6)=-3+(-5)/(x+6)`

∴ The quotient is x - 3

∵
`(x^(2)+5x-20 )/(x+7)=x+(-2x-20)/(x+7)`

∵
`(-2x-20)/(x+7)=-2+(-6)/(x+7)`

∴ The quotient is x - 2

∵
`(x^(2)+13x+54 )/(x+6)=x+(7x+54)/(x+6)`

∵
`(7x+54)/(x+6)=7+(12)/(x+6)`

∴ The quotient is x + 7