Question

Find the factors of function f. Fx = x4 – 5x3 – 4x2 + 20x
Based on the factors, which statement is true about the graph of function f?

Answer 1

Answer: (D) The graph crosses the x-axis at the point (2,0)

Step-by-step explanation:

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Answer 2

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients. The correct option is C, The graph crosses the x-axis at the point (2,0).

What is a polynomial?

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.

Given the polynomial f(x) = x⁴ – 5x³ – 4x² + 20x.

The factorisation of the given polynomial can be written as,

f(x) = x⁴ – 5x³ – 4x² + 20x

Take x as the common term from the complete polynomial,

f(x) = x(x³ – 5x² – 4x + 20)

f(x) = x[x²(x - 5) -4 (x - 5)]

f(x) = x(x² - 4)(x - 5)

x = 0, ±2, 5

x = -2, 0, 2, 5

Since the factors of a polynomial intersect the x-axis at their respective values, therefore, the function will intersect the x-axis at (-2, 0), (0,0), (2, 0), and (5, 0).

Hence, Based on the factors, the statement that is true about the graph of function f(x) is The graph crosses the x-axis at the point (2,0).

Learn more about Polynomials:

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