Algebra Part 2 Flashcards
What is the identity element for addition?
0
What is the identity element for multiplication?
1
What is the first term in the expansion of (x+y)^n?
x^n
What is the last term in the expansion of (x+y)^n?
y^n
State the Inverse Property for addition.
a + (-a) = 0
State the Inverse Property for multiplication.
a • (1/a) = 1
What is the sum of exponents in every term of (x+y)^n?
n
How many terms are in the expansion of (x+y)^n?
n + 1
How does the exponent of x change in the expansion of (x+y)^n?
Decreases by 1, term by term from n to 0
How does the exponent of y change in the expansion of (x+y)^n?
Increases by 1, term by term from 0 to n
What is true about the coefficients of terms equidistant from the ends in the expansion of (x+y)^n?
They are equal
What is the Distributive Property?
a(b + c) = ab + ac and (a + b)c = ac + bc
Define ‘Common factor’.
Factors shared or common of two or more numbers
What is the Lowest Common Factor?
The lowest number common to two or more numbers
What is the formula for the coefficient of the next term in a binomial expansion?
C = AB/(D+1)
What does LCM stand for?
Least Common Multiple
What is the LCM of two natural numbers?
The smallest natural number that has both as a factor
What is the formula for the rth term in (x+y)^n?
rth term = (nCr)x^(n-r)y^r
What is the Least Common Denominator (LCD)?
The smallest integer that contains both b and d as a factor
What is the Greatest Common Factor (GCF)?
The largest integer which is a factor of each of the given numbers
What is the relationship between HCF and LCM of two numbers?
Product of Two Numbers = (HCF)(LCM)
What is a multiple of a number?
The product that the number gives when multiplied by a counting or natural number
How do you find the sum of the coefficients in the expansion of (ax + by +…)?
Substitute 1 to every variable and simplify
What is the sum of exponents in the expansion of (ax + by +…)^n?
n(n + 1)
What is Pascal’s Triangle?
An array of numbers in the shape of an isosceles triangle, with 1 at the top and ends of each line, with other numbers formed by adding the closest pair above
What does the Remainder Theorem state?
If a polynomial is divided by (x - k), the remainder equals f(k)
State the Fundamental Theorem of Algebra.
Every single-variable polynomial with complex coefficients has at least one complex root
Expand (x+y)^5.
x^5 + 5x^4y + 10x^3y^2 + 10x^2y^3 + 5xy^4 + y^5
