Question

How do I factor a polynomial completely through grouping?

Answer 1

Hint: Polynomial: A polynomial is an expression of variables that involves only the operations of multiplication, addition, subtraction, and division of variables.
Type of polynomial:
I. Monomial
II. Binomial
III. Trinomial

Complete step by step solution:
To solve it, let’s take a polynomial,
$ {a^3} + 4{a^2} + 3 $
Now follow the steps to factorize it:
Step 1: Divide the polynomial into two groups: first half and second half.
$ {a^3} + 3{a^2} + a + 3 $
Step 2: factor the GCF out of the first and factor the GCF out of the second.
$ \left( {{a^3} + 3{a^2}} \right) + \left( {a + 3} \right) $
Step 3: you should have a common binomial/trinomial factor.
$ {a^2}\left( {a + 3} \right) + \left( {a + 3} \right) $
Step 4: factor out the common binomial/trinomial factor.
$ \left( {{a^2} + 1} \right)\left( {a + 3} \right) $
By following the above maintenance step we can do the complete factor of polynomial by grouping.

Note: Polynomials are used in our daily life to make complex problems simpler. This is used in field of finance, electronics, curve fitting, chemistry, and physics as well engineering. To solve complex polynomials we factorize it to get a solution of that polynomial at time of solving the polynomial we should make the polynomial equation equal to zero.