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 \(3x^{2} — 2x + 3x — 2\).

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

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

\(=x(3x-2)+1(3x-2)\)

As, the binomial \((3x — 2)\) is the common factor of the polynomial.

The polynomial can be factorized as,

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

\(= (3x-2)(x+1)\)

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

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 \(3x^{2} — 2x + 3x — 2\).

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

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

\(=x(3x-2)+1(3x-2)\)

As, the binomial \((3x — 2)\) is the common factor of the polynomial.

The polynomial can be factorized as,

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

\(= (3x-2)(x+1)\)

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