Answer:
The leading term of the given polynomial equation is (0.1)x³ ⇒ (B)
Step-by-step explanation:
To find the polynomial equation from its graph search about
- x-intercepts (values x at y = 0)
- y-intercept (value y at x = 0)
- Use the x-intercepts to find its factors
- The product of its factors gives the terms of the polynomial equation
- If the x-intercepts of the graph are (a, 0) and (m, 0) then the factors of it are (x - a) and (x - m), then the polynomial is y = (x - a)(x - m)
From the given graph
∵ There are three x-intercepts (-2, 0), (0, 0), (4, 0)
→ That means the polynomial equation has 3 factors use the
x-intercepts to find them
∵ The x intercept is (-2, 0)
∴ x = -2
→ Add 2 to both sides
∴ x + 2 = -2 + 2
∴ x + 2 = 0
→ That means the equation has a factor (x + 2)
∴ (x + 2) is a factor of the given polynomial equation
∵ The x intercept is (4, 0)
∴ x = 4
→ Sutract 4 from both sides
∴ x - 4 = 4 - 4
∴ x - 4 = 0
→ That means the equation has a factor (x - 4)
∴ (x - 4) is a factor of the given polynomial equation
∵ The x intercept is (0, 0)
∴ x = 0
∴ x is a factor of the given polynomial equation
→ To find the polynomial multiply its factors
∴ y = x( x + 2)(x - 4)
∵ The leading term is the first term
∵ x(x)(x) = x³ is the first term when we multiply the 3 factors
∴ The leading term is x³
→ The choices have (0.1)x³
∴ y = 0.1x(x + 2)(x - 4)
∴ The leading term of the given polynomial equation is (0.1)x³
