Answer

Verified

373.2k+ views

**Hint:**Here in this question, we have to find the factors of the given equation. If you see the equation it is in the form of \[{a^3} + {b^3}\]. We have a standard formula on this algebraic equation and it is given by \[{a^3} + {b^3} = (a + b)({a^2} - ab + {b^2})\], hence by substituting the value of a and b we find the factors.

**Complete step-by-step solution:**

The equation is an algebraic equation or expression, where algebraic expression is a combination of variables and constants.

Now consider the given equation \[{x^3} + 216\], let we write in the exponential form. The number \[{x^3}\] can be written as \[x \times x \times x\] and the \[216\]can be written as \[6 \times 6 \times 6\], in the exponential form it is \[{\left( 6 \right)^3}\]. The number \[{x^3}\] is written as \[x \times x \times x\] and in exponential form is \[{(x)^3}\]. Therefore, the given equation is written as \[{\left( x \right)^3} + {6^3}\], the equation is in the form of \[{a^3} + {b^3}\].The \[{a^3} + {b^3}\]have a standard formula on this algebraic equation and it is given by \[{a^3} + {b^3} = (a + b)({a^2} - ab + {b^2})\], here the value of a is \[x\] and the value of b is 6. By substituting these values in the formula, we have

\[{x^3} + 216 = {\left( x \right)^3} + {6^3} = (x + 6)({(x)^2} - (x)(6) + {6^2})\]

On simplifying we have

\[ \Rightarrow {x^3} + 216 = (x + 6)({x^2} - 6x + 36)\]

The second term of the above equation can be solved further by using factorisation or by using the formula \[\dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}\]

Let we consider \[{x^2} - 6x + 36\], and find factors for this. Here a=1, b=-6 and c=36. By substituting these values in the formula we get

\[x = \dfrac{{ - ( - 6) \pm \sqrt {{{( - 6)}^2} - 4(1)(16)} }}{{2(1)}}\]

On simplification we have

\[ \Rightarrow x = \dfrac{{6 \pm \sqrt {36 - 64} }}{2}\]

\[ \Rightarrow x = \dfrac{{6 \pm \sqrt { - 28} }}{2}\]

On further simplifying we get an imaginary number so let us keep as it is.

Therefore, the factors of \[{x^3} + 216\] is \[(x + 6)({x^2} - 6x + 36)\]

**Note:**To find the factors for algebraic equations or expressions, it depends on the degree of the equation. If the equation contains a square then we have two factors. If the equation contains a cube then we have three factors. Here this equation also contains 3 factors, the two factors are imaginary.

Recently Updated Pages

If O is the origin and OP and OQ are the tangents from class 10 maths CBSE

Let PQ be the focal chord of the parabola y24ax The class 10 maths CBSE

Which of the following picture is not a 3D figure a class 10 maths CBSE

What are the three theories on how Earth was forme class 10 physics CBSE

How many faces edges and vertices are in an octagonal class 10 maths CBSE

How do you evaluate cot left dfrac4pi 3 right class 10 maths CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Write the 6 fundamental rights of India and explain in detail

Name 10 Living and Non living things class 9 biology CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths