Question

Which Polynomial factored completely

g^5-g
4g^3+18^2+20g
24g^2-6g^4
2g^2+5g+4

Answer 1

Out of the given polynomials, g^5-g is factored completely as g(g^4-1)=g(g^2+1)(g-1)(g+1), and 2g^2+5g+4 is factored as (2g+4)(g+1).

Step-by-step explanation:

The question asks which polynomial is factored completely. The polynomials given are:

• g^5-g
• 4g^3+18^2+20g
• 24g^2-6g^4
• 2g^2+5g+4

Let's examine each one:

1. g^5-g can be factored by taking g as a common factor: g(g^4-1) = g(g^2+1)(g-1)(g+1).
2. 4g^3+18^2+20g doesn't seem to have correct terms (18^2 seems to be a typo) so we cannot proceed with that one.
3. 24g^2-6g^4 can be factored by factorization: -6g^4+24g^2 = -6g^2(g^2-4) = -6g^2(g-2)(g+2).
4. 2g^2+5g+4 can be factored into (2g+4)(g+1) by finding the two numbers that multiply to give 8 (product of the quadratic coefficient and the constant term) and add to give 5 (the linear coefficient).

Out of the options provided, the completely factored polynomials are g^5-g and 2g^2+5g+4.