Math virtual assistant

Calculators Topics Go Premium About Snapxam
ENGESP
Topics

Synthetic division of polynomials Calculator

Get detailed solutions to your math problems with our Synthetic division of polynomials step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here!

Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

1

Solved example of synthetic division of polynomials

$\lim_{x\to{\left(-1\right)}}\left(\frac{x^4+2x^3+x^2}{x+1}\right)$
2

We can factor the polynomial $x^4+2x^3+x^2$ using synthetic division (Ruffini's rule). We found that $-1$ is a root of the polynomial

${\left(-1\right)}^4+2\left({\left(-1\right)}^3\right)+{\left(-1\right)}^2=0$
3

Let's divide the polynomial by $x+1$ using synthetic division. First, write the coefficients of the terms of the numerator in descending order. Then, take the first coefficient $1$ and multiply by the factor $-1$. Add the result to the second coefficient and then multiply this by $-1$ and so on

$\left|\begin{array}{c}1 & 2 & 1 & 0 & 0 \\ & -1 & -1 & 0 & 0 \\ 1 & 1 & 0 & 0 & 0\end{array}\right|-1$
4

In the last row of the division appear the new coefficients, with remainder equals zero. Now, rewrite the polynomial (a degree less) with the new coefficients, and multiplied by the factor $x+1$

$\lim_{x\to-1}\left(\frac{\left(x^{3}+x^{2}\right)\left(x+1\right)}{x+1}\right)$
5

Simplify the fraction by $x+1$

$\lim_{x\to-1}\left(x^{3}+x^{2}\right)$
6

Factor by $x^{2}$

$\lim_{x\to-1}\left(x^{2}\left(x+1\right)\right)$
7

Evaluating the limit when $x$ tends to $-1$

$\left({\left(-1\right)}^{2}\right)\left(-1+1\right)$
8

Simplifying

$0$

Struggling with math?

Access detailed step by step solutions to millions of problems, growing every day!