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Simplify the expression $\frac{5x^3-4x^2+7x-8}{x-3}$

Step-by-step Solution

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Final Answer

$5x^{2}+11x+40+\frac{112}{x-3}$
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Step-by-step Solution

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1

Let's divide the polynomial by $x-3$ using synthetic division (also known as Ruffini's rule). First, write all the coefficients of the polynomial in the numerator in descending order based on grade (putting a zero if a term doesn't exist). Then, take the first coefficient ($5$) and multiply it by the root of the denominator ($3$). Add the result to the second coefficient and multiply this by $3$ and so on

$\left|\begin{matrix}5 & -4 & 7 & -8 \\ & 15 & 33 & 120 \\ 5 & 11 & 40 & 112\end{matrix}\right|3$
2

In the last row appear the new coefficients of the polynomial. Use these coefficients to rewrite the new polynomial with a lower grade, and the remainder ($112$) divided by the divisor

$5x^{2}+11x+40+\frac{112}{x-3}$

Final Answer

$5x^{2}+11x+40+\frac{112}{x-3}$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SimplifyWrite in simplest formFactorFactor by completing the squareFind the integralFind the derivativeFind (5x^3+-4x^2)/(x-3) using the definitionSolve by quadratic formula (general formula)Find the rootsFind break even pointsFind the discriminant

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Function Plot

Plotting: $5x^{2}+11x+40+\frac{112}{x-3}$

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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
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Main Topic: Polynomial long division

In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalised version of the familiar arithmetic technique called long division.

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