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 \(x^{3}—7x^{2}+4x-28\).

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

\(x^{3}-7x^{2}+4x-28=(x^{3}-7x^{2})+(4x-28)\)

\(=x^{2}(x-7)+4(x-7)\)

As, \((x-7)\) is the common factor of the polynomial,

The polynomial can be factorized as,

\(x^{3}-7x^{2}+4x-28=x^{2}(x-7)+4(x-7)\)

\(=(x-7)(x^2+4)\)

Therefore, the factorization of the polynomial is \((x — 7)(x^{2} +4)\).

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 \(x^{3}—7x^{2}+4x-28\).

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

\(x^{3}-7x^{2}+4x-28=(x^{3}-7x^{2})+(4x-28)\)

\(=x^{2}(x-7)+4(x-7)\)

As, \((x-7)\) is the common factor of the polynomial,

The polynomial can be factorized as,

\(x^{3}-7x^{2}+4x-28=x^{2}(x-7)+4(x-7)\)

\(=(x-7)(x^2+4)\)

Therefore, the factorization of the polynomial is \((x — 7)(x^{2} +4)\).