Polynomials and the Binomial Theorem flashcards
16 practice cards drawn from the Polynomials and the Binomial Theorem lessons. Tap a card to turn it over. Every answer is checked against the lesson it came from.
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What are the coefficients of ?
1, 2, 1
from “The Binomial Theorem”
What is the coefficient of in ?
10
from “The Binomial Theorem”
What are the first three terms of ?
from “Binomial Series for a Negative or Fractional Index”
What are the first three terms of ?
from “Binomial Series for a Negative or Fractional Index”
For which x is the expansion of valid?
|x| < 4
from “Expanding (a + bx) to a Rational Power”
What are the first two terms of ?
from “Expanding (a + bx) to a Rational Power”
. What is the remainder when divided by (x − 5)?
34
from “Factor and Remainder Theorem”
. What is the remainder when divided by (x − 4)?
20
from “Factor and Remainder Theorem”
One root of is 1. What are the other two?
-2 and 4
from “Solving a Cubic Completely”
One root of is 2. What are the other two?
-1 and -3
from “Solving a Cubic Completely”
For , what is ?
6
from “Roots and Coefficients of a Cubic”
For cx + d = 0, what does equal?
from “Roots and Coefficients of a Cubic”
Why does substituting the reverse transformation work?
y solves the new equation exactly when the old root is reached
from “Transforming the Roots of a Polynomial”
To build an equation whose roots are , what do you substitute?
from “Transforming the Roots of a Polynomial”
Expand (x + 2)(x + 1)(x + 5). What is the constant term?
10
from “Expanding Three Binomials”
Expand (x + 3)(x + 4)(x + 1). What is the coefficient of ?
8
from “Expanding Three Binomials”