How do you divide (x^3+15x^2+45x-25)div(x+5) using synthetic division?

2 Answers
Aug 12, 2018

(x^3+15x^2+45x-25)/(x+5)=x^2+10x-5

Explanation:

(x^3+15x^2+45x-25)/(x+5)

=(x^2(x+5)+10x^2+45x-25)/(x+5)

=(x^2(x+5)+10x(x+5)-5x-25)/(x+5)

=(x^2cancel((x+5))+10xcancel((x+5))-5cancel((x+5)))/cancel((x+5))

=x^2+10x-5

\0/ Here's our answer !

Aug 12, 2018

(x^3+15x^2+45x-25)=(x+5)(x^2+10x-5 )+(0)

Explanation:

(x^3+15x^2+45x-25)div(x+5)

Using synthetic division :

We have , p(x)=(x^3+15x^2+45x-25) and "divisor : " x=-5

We take ,coefficients of p(x) to 1,15,45,-25

-5| 1color(white)(.......)15color(white)(........)45color(white)(.....)-25
ulcolor(white)(....)| ul(0color(white)( ....)-5color(white)(....)-50color(white)(..........)25
color(white)(......)1color(white)(........)10color(white)(....)-5color(white)(..........)color(violet)(ul|0|
We can see that , quotient polynomial :

q(x)=x^2+10x-5 and"the Remainder"=0

Hence ,

(x^3+15x^2+45x-25)=(x+5)(x^2+10x-5 )+(0)