the polynomial (2x^{3}-5x^{2}+4x - 10) is split into two groups, (2x^{3}+4x) and (-5x^{2}-10). the gcfs of…

the polynomial (2x^{3}-5x^{2}+4x - 10) is split into two groups, (2x^{3}+4x) and (-5x^{2}-10). the gcfs of each group is then factored out.\nwhat is the common binomial factor between the two groups after their gcfs have been factored out?\n(2x + 5)\n(2x-5)\n(x^{2}-2)\n(x^{2}+2)

the polynomial (2x^{3}-5x^{2}+4x - 10) is split into two groups, (2x^{3}+4x) and (-5x^{2}-10). the gcfs of each group is then factored out.\nwhat is the common binomial factor between the two groups after their gcfs have been factored out?\n(2x + 5)\n(2x-5)\n(x^{2}-2)\n(x^{2}+2)

Answer

Explanation:

Step1: Factor out GCF from (2x^{3}+4x)

Factor out (2x) from (2x^{3}+4x). Using the distributive property (ab + ac=a(b + c)), we have (2x(x^{2}+2)) since (\frac{2x^{3}}{2x}=x^{2}) and (\frac{4x}{2x} = 2).

Step2: Factor out GCF from (-5x^{2}-10)

Factor out (- 5) from (-5x^{2}-10). Using the distributive property (ab+ac=a(b + c)), we get (-5(x^{2}+2)) since (\frac{-5x^{2}}{-5}=x^{2}) and (\frac{-10}{-5}=2).

Answer:

(x^{2}+2)