Formula used:

The factors of a polynomial can be found 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 \(2z^{3}+8z^{2}+5z+20\).

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

\(2z^{3}+8z^{2}+5z+20 = (2z^{3}+8z^{2})+(5z+20)\)

\(=2z^{2}(z+4)+5(z+4)\)

As, \((z+4)\) is the common factor of the polynomial,

The polynomial can be factorized as,

\(2z^{3}+8z^{2}+5z+20 = 2z^{2}(z+4)+5(z+4)\)

\(=(z+4) (2z^{2}+5)\)

Therefore, the factorization of the polynomial is \((z+4) (2z^{2}+5)\).

The factors of a polynomial can be found 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 \(2z^{3}+8z^{2}+5z+20\).

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

\(2z^{3}+8z^{2}+5z+20 = (2z^{3}+8z^{2})+(5z+20)\)

\(=2z^{2}(z+4)+5(z+4)\)

As, \((z+4)\) is the common factor of the polynomial,

The polynomial can be factorized as,

\(2z^{3}+8z^{2}+5z+20 = 2z^{2}(z+4)+5(z+4)\)

\(=(z+4) (2z^{2}+5)\)

Therefore, the factorization of the polynomial is \((z+4) (2z^{2}+5)\).