Question

What is the product of the polynomials $(6{{x}^{3}}+3x)({{x}^{2}}+4)$ ?

Answer 1

Hint: We are given the polynomial in two terms and we need to find the products of the two brackets. We know how to operate polynomials and we just need to multiply each term of the bracket with all others.

Complete step-by-step solution:
When we find the product of any two polynomials, we just multiply each term of the first polynomial by each term of the second polynomial then simplify.
To multiply two polynomials, multiply each term of the first polynomial by each term of the second polynomial.
So now we are the polynomial as $(6{{x}^{3}}+3x)({{x}^{2}}+4)$
Now what we need to do is we will take the first term of first bracket and then multiply it will both the terms of the second bracket and similarly we will take the second term of the first bracket and multiply with both the terms of the second bracket and what we will get is:
$6{{x}^{5}}+24{{x}^{3}}+3{{x}^{3}}+12x$ and this is what we got as the new polynomial after doing product. Now we need to simplify this as we can clearly see that terms with the same degree are present and we can add them and then get the simplified form with a single term of the same degree and an easily readable polynomial in which we can easily do changes and apply various operations as and when needed.
So, the simplified polynomial which is the product of two polynomials given is:
$6{{x}^{5}}+27{{x}^{3}}+12x$

Note: While writing the last answer don’t forget to simplify the polynomial. Do the multiplication using one term of the first bracket at a time in order to avoid mistakes which lead to more confusion and wrong use of concepts.