Question

Answer the following using synthetic division? (5x²-17x-15) ÷ (x-4)

Answer 1

`(5x^2-17x-15)=(x-4)(5x+3)+(-3)`

Explanation:

Using synthetic division :

`diamond(5x^2-17x-15)div(x-4)`

We have , `p(x)=5x^2-17x-15 and "divisor :"x=4`

We take ,coefficients of `p(x) to 5,-17,-15`

. `4 |` `5color(white)(.....)-17color(white)(..)-15`
`ulcolor(white)(...)|` `ul(0color(white)( ..........)20color(white)(........)12`
`color(white)(......)5color(white)(..........)3color(white)(.......)color(violet)(ul|-3|`
We can see that , quotient polynomial :

`q(x)=5x+3 and"the Remainder"=-3`

Hence ,

`(5x^2-17x-15)=(x-4)(5x+3)+(-3)`