Question

What is the remainder when the polynomial 5x2+10x−15 is divided by x + 5?

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Answer 1

The remainder is 60.

Explanation:

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Answer 2

Given equation is
`\frac{{5x^(2)}+10x-15}{x+5}`

Solution:

We will divide the leading coefficients of the numerator and divisor

=
`(5x^(2))/(x)=5x` so, quotient is 5x

Multiplying divisor x+5 by 5x we have
`5x^(2)+25x`

We will now subtract
`5x^(2)+25x` from
`5x^(2)+10x-15` and we get the new remainder as
`-15x-15`

`\frac{{5x^(2)}+10x-15}{x+5}` becomes
`5x+(-15x-15)/(x+5)`

Now again divide the leading coefficient of numerator with x

`(-15x)/(x)=-15` new quotient is -15.

Now multiplying x+5 by -15 =
`-15x-75`

We will subtract this
`-15x-75` from -15x-15 to get a new remainder

Now remainder becomes 60

So,
`(-15x-15)/(x+5)=-15+(60)/(x+5)`

The new equation becomes =
`5x-15+(60)/(x+5)`

The remainder is 60.