Question

example 4

john graphed the function \\(f(x) = 2x^3 + 5x^2 - 28x - 15\\) and his friend jose graphed the function \\(g(x) = (x + 4)(x + 1)(x - 2)(x - 4)\\). whose function has more zeros?

solution

zeros of a function are the values of \\(x\\) which make the function equal to zero.

johns function, \\(f(x) = 2x^3 + 5x^2 - 28x - 15\\)

value: 1

find the degree of johns function.

a. 1
b. 2
c. 3
d. 4

Explanation:

Identify the polynomial function

The function given for John is:

$$f(x) = 2x^3 + 5x^2 - 28x - 15$$

Determine the highest exponent of the variable

The terms of the polynomial are \(2x^3\), \(5x^2\), \(-28x\), and \(-15\). The exponents of \(x\) in these terms are \(3\), \(2\), \(1\), and \(0\) respectively. The highest exponent is \(3\).

State the degree of the polynomial

The degree of a polynomial is the highest exponent of its variable. Therefore, the degree of John's function is \(3\).

Answer:

• a. 1
• b. 2
• c. 3 (Correct answer)
• d. 4