Leading coefficient — Algebra II, what it means and where it is taught

The number in front of the highest power. Its sign decides which way the right end goes.

Taught in Algebra II.

Where it is taught

Practise this idea

3 questions in the course bank use Leading coefficient, in Polynomial Functions & Their Graphs, Rational Expressions & Equations.

Problem 1

Write a polynomial of least degree with roots -2, 1 and 4, leading coefficient 1. Give it factored.

Worked answer

(x+2)(x-1)(x-4)

Root -2 gives (x+2)

Root 1 gives (x-1)

Root 4 gives (x-4)

Problem 2

Write the factored polynomial of least degree that touches at x=2 and crosses at x=-3, leading coefficient 1.

Worked answer

(x-2)^2(x+3)

Touch at 2 means (x-2)2

Cross at -3 means (x+3)

Problem 3

What is the horizontal asymptote of y=3x+2x-4?

  1. y=3
  2. y=0
  3. y=4
  4. There is none
Worked answer

y=3

Equal degrees, so take the ratio of the leading coefficients

31=3

Elsewhere

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