Factor by completing the square $\frac{x^3+12x^2+32x-45}{x+7}$

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Final answer to the problem

$\frac{\left(x^{2}+13x+45\right)\left(x-1\right)}{x+7}$
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Step-by-step Solution

How should I solve this problem?

  • Factor by completing the square
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Prove from LHS (left-hand side)
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1

We can factor the polynomial $x^3+12x^2+32x-45$ using the rational root theorem, which guarantees that for a polynomial of the form $a_nx^n+a_{n-1}x^{n-1}+\dots+a_0$ there is a rational root of the form $\pm\frac{p}{q}$, where $p$ belongs to the divisors of the constant term $a_0$, and $q$ belongs to the divisors of the leading coefficient $a_n$. List all divisors $p$ of the constant term $a_0$, which equals $-45$

$1, 3, 5, 9, 15, 45$

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$1, 3, 5, 9, 15, 45$

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Learn how to solve polynomial factorization problems step by step online. Factor by completing the square (x^3+12x^232x+-45)/(x+7). We can factor the polynomial x^3+12x^2+32x-45 using the rational root theorem, which guarantees that for a polynomial of the form a_nx^n+a_{n-1}x^{n-1}+\dots+a_0 there is a rational root of the form \pm\frac{p}{q}, where p belongs to the divisors of the constant term a_0, and q belongs to the divisors of the leading coefficient a_n. List all divisors p of the constant term a_0, which equals -45. Next, list all divisors of the leading coefficient a_n, which equals 1. The possible roots \pm\frac{p}{q} of the polynomial x^3+12x^2+32x-45 will then be. Trying all possible roots, we found that 1 is a root of the polynomial. When we evaluate it in the polynomial, it gives us 0 as a result.

Final answer to the problem

$\frac{\left(x^{2}+13x+45\right)\left(x-1\right)}{x+7}$

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Function Plot

Plotting: $\frac{\left(x^{2}+13x+45\right)\left(x-1\right)}{x+7}$

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3
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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 Factorization

They are a group of techniques that help us rewrite polynomial expressions as a product of factors.

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