maths -polynomials

Polynomial in one variable

an algebraic expression in which the variable has only non-negative integer powers.

Degree of a polynomial

the highest power of the variable in the polynomial.

Linear polynomial

A polynomial of degree 1.

Quadratic polynomial

A polynomial of degree 2.

Cubic polynomial

A polynomial of degree 3.

General form of a linear polynomial

ax + b

General form of a quadratic polynomial

ax² + bx + c

General form of a cubic polynomial

ax³ + bx² + cx + d

Value of a polynomial p(x) at x=k

The value obtained by replacing x by k in p(x)

Zero of a polynomial

A real number k is said to be a zero of a polynomial p(x) if p(k)=0.

Zero of a linear polynomial ax+b

-b/a.

Graph of a linear polynomial ax+b

A straight line.

The x-coordinate of the point where the graph of y = ax + b intersects the x-axis

represents the zero of the polynomial ax + b.

Graph of a quadratic polynomial ax² + bx + c

A parabola

The x-coordinates of the points where the graph of y = ax² + bx + c intersects the x-axis

represents the zeroes of the polynomial ax² + bx + c.

A quadratic polynomial can have at most 2 zeroes.