Summary Cubic polynomials - long division, synthetic division, and inspection

Cubic polynomials and equations
:




Long division :




step-by-step :




3+22+3
Example
:
divide ✗
by x I
-




1 .
I -
I 23+22+0×+3 -
must have of ;xZ;x ; constant
-




> . ~µf >
÷ IT 23+22+0×+3
E- I
¥ +22+0×+3
-



g.




✗
←



/
-

His xD -




3 .


#
.


2×2 +
Ox

a- , 23+22+0×+3 -


(2×2-22)
,
I> Is -22 '



2×+3
>
2×-2
I
a.
2- I 23+22+0×+3 35+2×+2 ] Factor / answer


-


(23-5) to .
2- I 23+22+0×+3
a


2×2 -

His xD -




> i.
a


2×2 +
Ox

2×+4 -


(2×2-22)
5. 2- I 23+22+0×+3 '



2×+3
-


(2×-2)
a




22£
-




5) remainder




(x3+x
>
3) ÷ Ex 13=>5+2×+2 5
-



+
-


. .
rem .




6.
I T -


x
>
+22+0×+3


s If
xD
-




a


2×2 +03C Example
:




222 -23C f- ( 2×3-3>5-11×+6
I. Divide
by 2+2
=




2=2-7×-3
+23C 2+22×3 -3×2-11×+6
7. 2- I 23+22+0×+3 -

(2×3+4×2)
-


(23-22) .
-7×2-112
a


2×2 +
Osc -


(-7×2 -
tax )
-


(2×2-22) .
3×+6

2x (3×+6)
'
-




0




nt①+Z
.




. :(2×3-3>(2-11×+0) :-(✗ + 2) =
2×2-7×+3

•
a- I
-
23+22+0×+3
-

His xD -




a


2×2 +
Ox




23£
'