Polynomials and the Binomial Theorem flashcards

14 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 (a + b)^2?

1, 2, 1

from “The Binomial Theorem”

What is the coefficient of in (1 + x)^5?

10

from “The Binomial Theorem”

What are the first three terms of (1 + x)⁻4?

1 − 4x + 10x²

from “Binomial Series for a Negative or Fractional Index”

What are the first three terms of (1 + x)⁻3?

1 − 3x + 6x²

from “Binomial Series for a Negative or Fractional Index”

For which x is the expansion of (12 + 3x)⁻¹ valid?

|x| < 4

from “Expanding (a + bx) to a Rational Power”

What are the first two terms of (16 + x)^½?

4 + x/8

from “Expanding (a + bx) to a Rational Power”

f(x) = x² + 9. What is the remainder when divided by (x − 5)?

34

from “Factor and Remainder Theorem”

f(x) = x² + 4. What is the remainder when divided by (x − 4)?

20

from “Factor and Remainder Theorem”

One root of f(x) = x³ − 3x² − 6x + 8 is 1. What are the other two?

-2 and 4

from “Solving a Cubic Completely”

One root of f(x) = x³ + 2x² − 5x − 6 is 2. What are the other two?

-1 and -3

from “Solving a Cubic Completely”

For x³ − 6x² + 11x − 6 = 0, what is α + β + γ?

6

from “Roots and Coefficients of a Cubic”

α+β+γ = 5 and αβ+βγ+γα = 6. What is α² + β² + γ²?

13

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?

x = y/2

from “Transforming the Roots of a Polynomial”

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