MICRO LESSON 1
What Is a Polynomial?
Picture it:
A polynomial is like a sentence made from numbers, variables and powers.
Simple:
A polynomial is an algebraic expression where variable powers are whole numbers.
Example:
3x² + 2x - 5.
Quick Check:
Is 1/x a polynomial?
MICRO LESSON 2
Terms and Coefficients
Picture it:
Each part separated by plus or minus is a term.
Simple:
A coefficient is the number multiplying the variable.
Example:
In 5x² - 3x + 7, coefficients are 5 and -3.
Quick Check:
What is the coefficient of x in 4x²-9x+1?
MICRO LESSON 3
Degree of a Polynomial
Picture it:
The highest power tells how complex the polynomial is.
Simple:
The degree is the highest exponent with a non-zero coefficient.
Example:
7x³+2x has degree 3.
Quick Check:
What is the degree of 5x⁴+2?
MICRO LESSON 4
Types by Number of Terms
Picture it:
One term, two terms and three terms have special names.
Simple:
Monomial has one term, binomial two, trinomial three.
Example:
5x is monomial; x+2 binomial; x²+x+1 trinomial.
Quick Check:
Classify x²-9.
MICRO LESSON 5
Value of a Polynomial
Picture it:
Substitute a number for x and calculate.
Simple:
The value of p(x) at x=a is found by replacing x with a.
Example:
If p(x)=x²+2x, p(3)=9+6=15.
Quick Check:
Find p(2) for p(x)=x+5.
MICRO LESSON 6
Zero of a Polynomial
Picture it:
A zero is the input that makes the polynomial output zero.
Simple:
a is a zero of p(x) if p(a)=0.
Example:
For p(x)=x-4, zero is 4.
Quick Check:
What is the zero of x+7?
MICRO LESSON 7
Remainder Idea
Picture it:
When a polynomial is divided by x-a, the remainder equals p(a).
Simple:
This is the remainder theorem.
Example:
For p(x)=x²+1 divided by x-2, remainder is p(2)=5.
Quick Check:
What is the remainder of x² divided by x-3?
MICRO LESSON 8
Algebraic Identities
Picture it:
Identities are shortcuts that work for all values.
Simple:
They help expand and factor expressions quickly.
Example:
(a+b)²=a²+2ab+b².
Quick Check:
Expand (x+3)².