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Sagot :
The degree of the polynomial formed is 6.
The degree of a polynomial is the highest degree of the variables present with non-zero coefficients.
For example the polynomial has three 7x³y²+9xy+4 terms. The first term has a degree of 5 (the sum of the powers 2 and 3), the second term has a degree of 1, and the last term has a degree of 0. Therefore, the polynomial has a degree of 5, which is the highest degree of any term.
Now the given functions are:
[tex]f(x)=x^3[/tex] ,g(x)=3x²-1 and h(x)=2x
Now we have to find (f ° g° h)(x). Let us first find (g°h)(x).
(g°h)(x) is equal to g[h(x)]
=g[2x+5]
=3(2x+5)²-1
=3(4x²+20x+25)-1
=12x²+60x+74
Now we find (f ° g° h)(x)
(f ° g° h)(x)=f[g(2x+5)]
f[g(2x+5)]=f(12x²+60x+74)
f(12x²+60x+74)=(12x²+60x+74)³
Now we have to simplify the expression:
(12x²+60x+74)³
=[tex]1728x^6+25920x^5+161568x^4+535680x^3+996336x^2+985680x+405224[/tex]
The largest degree of the variable x in the polynomial is 6.
hence the degree of [f o go h](x) is 6.
To learn more about degree of a function or polynomial visit:
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