Polynomial — Algebra I · Grade 9 or accelerated Grade 8, what it means and where it is taught
A sum of terms, each a number times a whole-number power of the variable.
Taught in Algebra I · Grade 9 or accelerated Grade 8.
Where it is taught
What uses it later
This idea is needed for:
- Binomial — A polynomial with two terms.
- Closure — Polynomials added, subtracted or multiplied always give another polynomial.
- Dividend — The polynomial being divided — the one inside the bracket.
- Divisor — The polynomial you are dividing by.
- Rational expression — A fraction whose top and bottom are polynomials.
Practise this idea
7 questions in the course bank use Polynomial, in Polynomial Operations, Polynomial Functions & Their Graphs, Limits & Continuity.
Problem 1
Polynomials are not closed under which operation?
- Division
- Addition
- Subtraction
- Multiplication
Worked answer
Division
x2 + 1x = x + 1x
That is not a polynomial
Problem 2
A rectangle has length x + 7 and width x - 3. Write its area as a polynomial.
Worked answer
x^2 + 4x - 21
(x + 7)(x - 3)
x2 - 3x + 7x - 21
= x2 + 4x - 21
Problem 3
What is the greatest number of turning points a degree 6 polynomial can have?
Worked answer
5
At most n-1 = 5
Problem 4
How many real roots can a degree 4 polynomial have at most?
Worked answer
4
Degree n gives at most n real roots
Problem 5
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 6
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 7
Find limx → 3(2x+1).
Worked answer
7
2(3)+1 = 7