Use synthetic division to solve ( x - x2 - 17x-15) =(x-5). what is the quotient?
x2 + 4x+3
o x² - 6x + 13 - 80
x3+4x2+3x
© x2-6x+13- 80
+5

(

5

x

2

−

17

x

−

15

)

=

(

x

−

4

)

(

5

x

+

3

)

+

(

−

3

)

Step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4