Question

Need to calculate:The factorization of the polynomial, \(3x^{2}-2x+3x-2\).

Answer 1

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 \((3x — 2) (x + 1)\).