Maths-chapter 2 Polynomials

Polynomial

An algebraic expression with whole number exponents on variables

Monomial

A polynomial with one term

Binomial

A polynomial with two terms

Trinomial

A polynomial with three terms

Degree of a polynomial

The highest power of the variable in a polynomial

Coefficient

The numerical factor of a term in a polynomial

Zero polynomial

The constant polynomial 0

Constant polynomial

A polynomial with no variable (like 2, -5, etc.)

Linear polynomial

A polynomial of degree 1 (e.g., ax + b)

Quadratic polynomial

A polynomial of degree 2 (e.g., ax² + bx + c)

Cubic polynomial

A polynomial of degree 3 (e.g., ax³ + bx² + cx + d)

Degree of zero polynomial

Not defined

Value of polynomial at x = a

Replace x with a in the expression

Zero of a polynomial

Any value of x for which p(x) = 0

Every linear polynomial

Has one and only one zero

A non-zero constant polynomial

Has no zero

The zero polynomial

Has every real number as its zero

x - a is a factor of p(x)

If p(a) = 0 (Factor Theorem)

p(x) = 0

Polynomial equation

Factorisation

Writing a polynomial as a product of two or more polynomials

Splitting the middle term

A method to factorise ax² + bx + c

(x + y)²

x² + 2xy + y²

(x - y)²

x² - 2xy + y²

x² - y²

(x + y)(x - y)

(x + a)(x + b)

x² + (a + b)x + ab

(x + y + z)²

x² + y² + z² + 2xy + 2yz + 2zx

(x + y)³

x³ + y³ + 3xy(x + y)

(x - y)³

x³ - y³ - 3xy(x - y)

x³ + y³ + z³ - 3xyz

(x + y + z)(x² + y² + z² - xy - yz - zx)

Factor of x³ - 23x² + 142x - 120

(x - 1)(x - 10)(x - 12)

Factor of y² - 5y + 6

(y - 2)(y - 3)

Factor of 6x² + 17x + 5

(3x + 1)(2x + 5)

Value of p(x) = 2x + 1 at x = -1

-1

Factor of 8x³ + 27y³ + 36x²y + 54xy²

(2x + 3y)³

Evaluate (104)³ using identity

1124864

Evaluate (999)³ using identity

997002999

Zero of x - 1

1

Zero of x + 2

-2

Zero of 2x + 1

-1/2

Zero of 3x - 2

2/3

Factor of x³ + 3x² + 5x + 6

x + 2

Factor of x² - 22x + 120

(x - 10)(x - 12)

Expanded form of (3a + 4b + 5c)²

9a² + 16b² + 25c² + 24ab + 40bc + 30ac

Expanded form of (4a - 2b - 3c)²

16a² + 4b² + 9c² - 16ab + 12bc - 24ac

(3a + 4b)³

27a³ + 64b³ + 108a²b + 144ab²

(5p - 3q)³

125p³ - 27q³ - 225p²q + 135pq²