Calculus/Algebra/Solutions
<
Calculus
|
Algebra
1. Simplify the expression
144
5
3
{\displaystyle 144^{\frac {5}{3}}}
144
5
3
=
(
2
4
⋅
3
2
)
5
3
=
2
20
3
⋅
3
10
3
=
2
6
2
2
3
⋅
3
3
3
3
=
1728
12
3
{\displaystyle 144^{\frac {5}{3}}=(2^{4}\cdot 3^{2})^{\frac {5}{3}}=2^{\frac {20}{3}}\cdot 3^{\frac {10}{3}}=2^{6}{\sqrt[{3}]{2^{2}}}\cdot 3^{3}{\sqrt[{3}]{3}}=1728{\sqrt[{3}]{12}}}
2. Factor
x
−
1
{\displaystyle x-1}
out of
6
x
3
−
4
x
2
+
3
x
−
5
{\displaystyle 6x^{3}-4x^{2}+3x-5}
.
:
6
x
2
+
2
x
+
5
x
−
1
)
6
x
3
−
4
x
2
+
3
x
−
5
−
(
6
x
3
−
6
x
2
)
_
2
x
2
+
3
x
−
5
−
(
2
x
2
−
2
x
)
_
5
x
−
5
−
(
5
x
−
5
)
_
0
{\displaystyle {\begin{array}{rl}&~~\,6x^{2}+2x+5\\x-1\!\!\!\!&{\big )}\!\!\!{\begin{array}{lll}\hline \,6x^{3}-4x^{2}+3x-5\end{array}}\\&\!\!\!\!-{\underline {(6x^{3}-6x^{2})~~~}}\\&\!\!\!\!~~~~~~~~~~~~2x^{2}+3x-5~~~\\&\!\!\!\!~~~~~~~~-{\underline {(2x^{2}-2x)~~~}}\\&\!\!\!\!~~~~~~~~~~~~~~~~~~~~~5x-5~~~\\&\!\!\!\!~~~~~~~~~~~~~~~~-{\underline {(5x-5)~~~}}\\&\!\!\!\!~~~~~~~~~~~~~~~~~~~~~~~~~~~~0~~~\\\end{array}}}
6
x
3
−
4
x
2
+
3
x
−
5
=
(
x
−
1
)
(
6
x
2
+
2
x
+
5
)
{\displaystyle \mathbf {6x^{3}-4x^{2}+3x-5=(x-1)(6x^{2}+2x+5)} }
![{\displaystyle 144^{\frac {5}{3}}=(2^{4}\cdot 3^{2})^{\frac {5}{3}}=2^{\frac {20}{3}}\cdot 3^{\frac {10}{3}}=2^{6}{\sqrt[{3}]{2^{2}}}\cdot 3^{3}{\sqrt[{3}]{3}}=1728{\sqrt[{3}]{12}}}](../../_assets_/eb734a37dd21ce173a46342d1cc64c92/e98ee45f312f7612a69fd555a25dfd9524576d2d.svg)
out of 
.
