# Need to calculate:The factorization of the polynomial, 3x^{2}-2x+3x-2. Question
Polynomial factorization Need to calculate:The factorization of the polynomial, $$3x^{2}-2x+3x-2$$. 2020-11-09
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 $$(3x — 2) (x + 1)$$.

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