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rosijanka [135]
3 years ago
11

What can be the leading term of the polynomial equation graphed below? answer choices(0.1)x4 (0.1)x^3 (-0.1)x^3 -(0.1)x^4​

Mathematics
1 answer:
almond37 [142]3 years ago
8 0

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

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