Formula used:

The factors of a polynomial can be find by taking a common factor and this method is calledcfactor by grouping,

\(ab ac+bd+cd=a(b+c)+d(b+c)\)

\(=(a+d)(b+c)\)

Or,

\(ab-ac+bd-cd=a(b-c)+d(b-c)\)

\(=(a+d)(b-c)\)

Calculation:

Consider the polynomial \(3x^{3}+2x^{2}+3x+2\).

This is a four term polynomial, factorization of this polynomial can be find by factor by grouping as,

\(3x^{3}+2x^{2}+3x+2=(3x^{3}+2x^{2})+(3x +2)\)

\(=x^{2}(3x+2)+1(3x+2)\)

As, \((3x + 2)\) is the common factor of the polynomial,

The polynomial can be factorized as,

\(x^{2}(3x+2)+1(3x+2)=(3x+2)(x^{2}+1)\)

Therefore, the factorization of the polynomial \(3x^{3}+2x^{2}+3x+2\) is \((3x+2) (x^{2}+1)\).

The factors of a polynomial can be find by taking a common factor and this method is calledcfactor by grouping,

\(ab ac+bd+cd=a(b+c)+d(b+c)\)

\(=(a+d)(b+c)\)

Or,

\(ab-ac+bd-cd=a(b-c)+d(b-c)\)

\(=(a+d)(b-c)\)

Calculation:

Consider the polynomial \(3x^{3}+2x^{2}+3x+2\).

This is a four term polynomial, factorization of this polynomial can be find by factor by grouping as,

\(3x^{3}+2x^{2}+3x+2=(3x^{3}+2x^{2})+(3x +2)\)

\(=x^{2}(3x+2)+1(3x+2)\)

As, \((3x + 2)\) is the common factor of the polynomial,

The polynomial can be factorized as,

\(x^{2}(3x+2)+1(3x+2)=(3x+2)(x^{2}+1)\)

Therefore, the factorization of the polynomial \(3x^{3}+2x^{2}+3x+2\) is \((3x+2) (x^{2}+1)\).