Question

F(x)=x+9, g(x)=x^2-4x, h(x)=x^4+2x^3

Answer 1

Answer:

The degree of (f × g × h)(x) is 7.

i.e option a ) 7

Step-by-step explanation:

Given:

$f(x)=(x+9)\\\\g(x)=(x^{2} -4x)\\\\h(x)=(x^{4}+2 x^{3})$

To Find:

Degree of (f × g × h)(x) = ?

Solution:

For multiplication of given function we require

Law of indices:

$(x^{a} )(x^{b} )=x^{(a+b)}$

Distributive Property:

(A + B)(C + D) = A (C + D) + B(C +D)

                      = AC + AD + BC +BD

Now,

$(f\times g\times h)(x) = (x+9)(x^{2} -4x)(x^{4} +2x^{3})\\ \\ =(x(x^{2} -4x) + 9(x^{2} -4x))(x^{4} +2x^{3})\\\\=(x^{3}+5x^{2}-36x)(x^{4} +2x^{3})\\\\=x^{7}+5x^{6}-36x^{5}+2x^{6}+10x^{5}-72x^{4}\\\\=x^{7} +7x^{6}-26x^{5}-72x^{4} \\\\\therefore (f\times g\times h)(x) = x^{7} +7x^{6}-26x^{5}-72x^{4}$

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.