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

naivlingr
2020-11-08
Answered

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

You can still ask an expert for help

Tuthornt

Answered 2020-11-09
Author has **107** answers

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,

$ab\u2014ac+bd\u2014cd=a(b\u2014c)+d(b-c)$

$=(a+d)(b-c)$

Calculation:

Consider the polynomial$3{x}^{2}\u20142x+3x\u20142$ .

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

$3{x}^{2}\u20142x+3x\u20142=(3{x}^{2}\u20142x)+(3x\u20142)$

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

As, the binomial$(3x\u20142)$ is the common factor of the polynomial.

The polynomial can be factorized as,

$3{x}^{2}\u20142x+3x-2=x(3x\u20142)+1(3x-2)$

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

Therefore, the factorization of the polynomial is$(3x\u20142)(x+1)$ .

The factors of a polynomial can be find by taking a common factor and this method is called factor by grouping,

Or,

Calculation:

Consider the polynomial

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

As, the binomial

The polynomial can be factorized as,

Therefore, the factorization of the polynomial is

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