Formula used:

The factors of a polynomial can be find by taking a common factor and this method is called factor 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 \(2x^{3}+6x^{2}+x+3\).

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

\(2x^{3}+6x^{2}+x+3=(2x^{3}+6x^{2})+(x+ 3)\)

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

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

The polynomial can be factorized as,

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

Therefore, the factorization of the polynomial \(2x^{3} + 6x^{2}+x+3\) is \((x + 3) (2x^{2}+1)\).

The factors of a polynomial can be find by taking a common factor and this method is called factor 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 \(2x^{3}+6x^{2}+x+3\).

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

\(2x^{3}+6x^{2}+x+3=(2x^{3}+6x^{2})+(x+ 3)\)

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

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

The polynomial can be factorized as,

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

Therefore, the factorization of the polynomial \(2x^{3} + 6x^{2}+x+3\) is \((x + 3) (2x^{2}+1)\).