Respuesta :
Answer:
The degree of (f × g × h)(x) is 7.
i.e option a ) 7
Step-by-step explanation:
Given:
[tex]f(x)=(x+9)\\\\g(x)=(x^{2} -4x)\\\\h(x)=(x^{4}+2 x^{3})[/tex]
To Find:
Degree of (f × g × h)(x) = ?
Solution:
For multiplication of given function we require
Law of indices:
[tex](x^{a} )(x^{b} )=x^{(a+b)}[/tex]
Distributive Property:
(A + B)(C + D) = A (C + D) + B(C +D)
= AC + AD + BC +BD
Now,
[tex](f\times g\times h)(x) = (x+9)(x^{2} -4x)(x^{4} +2x^{3})\\ \\ =(x(x^{2} -4x) + 9(x^{2} -4x))(x^{4} +2x^{3})\\\\=(x^{3}+5x^{2}-36x)(x^{4} +2x^{3})\\\\=x^{7}+5x^{6}-36x^{5}+2x^{6}+10x^{5}-72x^{4}\\\\=x^{7} +7x^{6}-26x^{5}-72x^{4} \\\\\therefore (f\times g\times h)(x) = x^{7} +7x^{6}-26x^{5}-72x^{4}[/tex]
Degree is highest power raised to the variable.
Therefore here highest power raised to the variable is 7
Therefore degree of (f × g × h)(x) is 7.
