Question

Lucas and Erick are factoring the polynomial 12x ^ 3 - 6x ^ 2 + 8x - 4 4. Lucas groups the polynomial (12x^ 3 + 8x)+(-6x^ 2 -4) to factor Erick groups the polynomial (12x ^ 3 - 6x ^ 2) + (8x - 4) to factor Who correctly grouped the terms to factor ? Explain .

Answer 1

Answer:

Both factor can correctly grouped the terms to factor.

Step-by-step explanation:

Given two polynomial,

$12x^3-6x^2+8x-4\hfill (1)$

$=(12x^3+8x)+(-6x^2-4)\hfill (2)$

$=(12x^3-6x^2)+(8x-4)\hfill (3)$

To choose correct factor among (2) and (3) of (1).

Consider (2) we get,

$(12x^3+8x)+(-6x^2-4)=4x(3x^2+2)-2(3x^2+2)=(4x-2)(3x^2+2)$

And from (3) we get,

$(12x^3-6x^2)+(8x-4)=3x^2(4x-2)+2(4x-2)=(3x^2+2)(4x-2)$

Since (2) and (3) gives same factor and both factors are irreducible and gives values of x directly so we can accept both factors as correct. In case we get different terms of factors in that case we must choose the simplest factor from which we can derive value of x easily.  

So both (2) and (3) can correctly grouped the terms to factor.