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A cubic polynomial is a type of polynomial with the highest power of the variable or degree to be <math>3</math>. Cubic polynomials are used in various areas of mathematics and science, including physics, engineering, and economics.

== Definition ==
A cubic polynomial is a polynomial with the highest exponent of a variable i.e. degree of a variable as <math>3</math>.  The general form of a cubic polynomial is  <math>ax^3+bx^2+cx+d=0</math>, <math>a \ne 0</math>, where <math>a,b,c</math> are coefficients and <math>d</math> is the constant with all of them being real numbers. An equation involving a cubic polynomial is called a cubic equation. 

Some of the examples of a cubic polynomial are 

<math>4x^3</math> , <math>2x^3+1</math> , <math>5x^3+x^2</math> , <math>2x^3+4x^2+6x+7</math>

== Example ==
Factorise  <math>x^3-23x^2+142x-120</math>

<math>x^3-23x^2+142x-120</math>

<math>x^3-x^2-22x^2+22x+120x-120</math>

<math>x^2(x-1)-22x(x-1)+120(x-1)</math>

<math>(x-1)(x^2-22x+120)</math>  Taking <math>(x-1)</math> common

Now factorise <math>x^2-22x+120</math>

<math>x^2-22x+120</math>

<math>x^2-10x-12x+120</math>

<math>x(x-10)-12(x-10)</math>

<math>(x-10)(x-12)</math>



<math>x^3-23x^2+142x-120=(x-1)(x-10)(x-12)</math>

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