# 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 $$(3x — 2) (x + 1)$$.

### Relevant Questions

Need to calculate:The factorization of the polynomial, $$2x^{4}+6x^{2}+5x^{2}+15$$.
Need to calculate:The factorization of $$3x^{3}+2x^{2}+3x+2$$.
Need to calculate:The factorization of $$x^{3}+3x^2+2x+6$$
Need to calculate:The factorization of the polynomial $$a^{2}+ac+a+c$$
Need to calculate: The factorization of the polynomial $$ax^{2}+ay+bx^{2}+by$$.
Need to calculate:The factorization of $$x^{3}+8x^{2}-3x-24$$.
Need to calculate:The factorization of $$x^{3}+4x^{2}+3x+12$$.
Need to calculate:The factorization of $$2x^{3}-8x^{2}-9x+36$$.
Need to calculate:The factorization of $$8x^{3}+20x^{2}+2x+5$$.
Need to calculate:The factorization of $$2x^{3}+6x^{2}+x+3$$.