Question

Select the correct answer from each drop-down menu. f(x) = x2 − 8x + 15 g(x) = x − 3 h(x) = f(x) ÷g(x)

Answer 1

h(x) = x-5 . The domain of h(x) is (- infinity,3)  U (3, infinity).

Answer 2

Selecting the correct value from each drop-down menu, the result of ratio of two equation is required. The value of h(x) is (x-5) and the domain is,

$h(x);(-\infty, 3) \cup (3, \infty)$

What is polynomial equation?

A polynomial equation is the equation in which the unknown variable is one and the highest power of the unknown variable is n.

Here, n is any real number.

Given information-

The given equation in the problem is,

$f(x)=x^2-8x+15$

$g(x)=x-3$

We have to find the ratio of the given equations as,

$h(x) = f(x) \div g(x)$

Put the values,

$h(x)=(x^2-8x+15)\div (x-3)$

The above equation can be written as,

$h(x)=\dfrac{(x^2-8x+15)}{ (x-3)}\\h(x)=\dfrac{(x^2-5x-3x+15)}{ (x-3)}\\h(x)=\dfrac{(x(x-5)-3(x-5))}{ (x-3)}\\h(x)=\dfrac{((x-5)(x-3))}{ (x-3)}\\\\h(x)=(x-5)$

The result of the division of two equation is (x-5). Here the given division is not gives the infinity value at the x equal to the 3. Thus domain of the h(x) is,

$h(x);(-\infty, 3) \cup (3, \infty)$

Hence, the value of h(x) is (x-5) and the domain is,

$h(x);(-\infty, 3) \cup (3, \infty)$

Learn more about the polynomial equation here;

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