Sokintahilzppsuidn
Answered

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f(x) = (x³+2) (x²+2)​

Sagot :

Martusjenylynidn

Answer:

The polynomial f(x) = (x³+2)(x²+2) can be factored as follows:

f(x) = (x³+2)(x²+2)

= (x³+2x²+2x+4)

= (x+1)(x²+1)(x+2)

Therefore, the factors of f(x) = (x³+2)(x²+2) are (x+1), (x²+1), and (x+2).

MrChrisidn

[tex]\underline{\underline{\large{\red{\mathcal{✒GIVEN:}}}}}[/tex]

[tex]\bullet \: \: \rm{f(x) = ( {x}^{3} + 2)( {x}^{2} + 2)}[/tex]

[tex]\underline{\underline{\large{\red{\mathcal{REQUIRED:}}}}}[/tex]

Simplify the equation.

[tex]\underline{\underline{\large{\red{\mathcal{SOLUTION:}}}}}[/tex]

To simplify the equation, let's expand using [tex]\tt{\purple{FOIL \: method}}[/tex] and [tex]\tt{\purple{Distributive \: Property}}[/tex]:

[tex]\tt{f(x) = ( {x}^{3} + 2)( {x}^{2} + 2)}[/tex]

[tex]\tt{f(x) = {x}^{3} ( {x}^{2} + 2) + 2( {x}^{2} + 2)}[/tex]

Now, let's apply Distributive Property:

[tex]\tt{f(x) = {x}^{3} ( {x}^{2} ) + {x}^{3} (2) + {2x}^{2} + 2(2)}[/tex]

[tex]\large{\tt{\purple{f(x) = {x}^{5} + 2 {x}^{3} + 2 {x}^{2} + 4}}}[/tex]

Final Answer:

[tex]\therefore[/tex] The simplified equation is [tex]\large{\boxed{\rm{\purple{f(x) = {x}^{5} + 2 {x}^{3} + 2 {x}^{2} + 4}}}}[/tex]