Question

Write each of the following in the product form.
$8{x^3}$

Answer 1

Hint: Polynomials are consisting of constants and variables. The Values of constant are fixed i.e. we know the value of constant e.g. 3, 7, 2 all are constant. The value of the variable is not fixed i.e. we don't know the value. When some is not given to us then we can assume that value by taking a variable e.g. x, y, z all are variables.
If any number has power 3 than it means that number is multiplied by itself 3 times and we say it as cube e.g. ${3^3} = 3 \times 3 \times 3 = 27$
If we have to find cube of variable than it can be written in the product as follows:
$ \Leftrightarrow {x^3} = x \times x \times x$

Complete step-by-step answer:
First of all, split them in constants and variables e.g. 4a. In 4a, 4 is the constant and a is variable.
Here, we have given a polynomial i.e. $8{x^3}$. In $8{x^3}$, 8 is the constant and ${x^3}$.
Moreover, x has power 3 means the cube of the x, hence we can write it as
$ \Leftrightarrow {x^3} = x \times x \times x$
The eight times ${x^3}$ is given by $8{x^3}$. So, we can write it as
$ \Leftrightarrow 8{x^3} = 8 \times x \times x \times x$
So, $8{x^3}$can be written in product form as $8 \times x \times x \times x$

Note: The three types of polynomial based on terms are discussed as follows:
Monomial: - If the number of terms in a polynomial is one then they are said to be Monomial. E.g. $4x,2{y^{}},{x^4}$etc.
Binomial: - If the number of terms in a polynomial are two then they are said to be Monomial. E.g. $6 + 2y,{x^2} + z$etc.
Trinomial: - If the number of terms in a polynomial are three then they are said to be Monomial. E.g. $6{x^3}y + {z^2} + 6xy,8{x^4} + z + 16$etc.