Q1: Factor the polynomial 6x4 + 24x3 − 72x2 completely by first factoring out the GCF, and then factoring the rest of the expression. Q2: Consider the polynomial 6x4 + 24x3 − 72x2. What is the greatest common factor (GCF) of the terms of the polynomial?

After factorizing the given polynomial we get 6x^2 (x+6)(x-2)

Step-by-step explanation:

Given Polynomial:  

6x^4+24x^3−72x^2

We need to completely factorize the polynomial.

Consider,

6x^4+24x^3−72x^2

GCF = 6x^2, By taking it common out

= 6x^2 (x^2+4x-12)

= 6x^2 (x^2+6x-2x-12)

= 6x^2 (x(x+6)-2(x+6))

= 6x^2 (x+6)(x-2)

Therefore, After factorizing the given polynomial we get 6x² ( x + 6 ) ( x - 2 )

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