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A polynomial is an algebraic expression of the form p(x) = a

where a

The real number that precedes the variable is called the coefficient.

A polynomial involving one variable is called a polynomial in one variable.

The exponent of the highest power of the variable of a polynomial is called the degree of the polynomial.

Based on its degree, a polynomial can be called as linear polynomial, quadratic polynomial, cubic polynomial and so on.

The polynomial with all the coefficients as zeros is called a zero polynomial.

A polynomial with a single term of a real number is called a constant polynomial.

A polynomial of degree one is called a first-degree or linear polynomial. The general form of a linear polynomial is ax + b, where a and b are real numbers and a â‰ 0.

A polynomial of degree two is called a second degree or quadratic polynomial. The general form of a quadratic polynomial is ax

A polynomial of degree three is called a third-degree or cubic polynomial. The general form of a cubic polynomial is ax

A polynomial of degree four is called a fourth-degree or biquadratic polynomial. The general form of a quadratic polynomial is ax

The value of a polynomial p(x) when x = k (k is a real number) is the value obtained by substituting x as k. It is denoted by p(k).

The zero of the polynomial is defined as any real value of x, for which the value of the polynomial becomes zero.

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

The zero of the polynomial is the x-coordinate of the point, where the graph intersects the x-axis. If a polynomial p(x) intersects the x-axis at ( k, 0), then k is the zero of the polynomial.

The graph of a linear polynomial intersects the x-axis at a maximum of one point. Therefore, a linear polynomial has a maximum of one zero.

The graph of a quadratic polynomial intersects the x-axis at a maximum of two points. Therefore, a quadratic polynomial can have a maximum of two zeroes. In this case the shape of the graph is a parabola. The shape of the parabola of a quadratic polynomial ax^{2} + bx + c, a â‰ 0 depends on a.

If a > 0, then the parabola opens upwards.

If a < 0, then the parabola opens downwards.

Geometrically a quadratic polynomial can have either two distinct zeroes or two equal zeroes or no zero. This indicates that a quadratic polynomial has almost 2 zeroes.

The graph of a cubic polynomial intersects the x-axis at maximum of three points. A cubic polynomial has a maximum of three zeroes.

In general, an n^{th}-degree polynomial intersects the x-axis at a maximum of n points. Therefore, an n^{th}-degree polynomial has a maximum of n zeroes.

A polynomial is an algebraic expression of the form p(x) = a

where a

The real number that precedes the variable is called the coefficient.

A polynomial involving one variable is called a polynomial in one variable.

The exponent of the highest power of the variable of a polynomial is called the degree of the polynomial.

Based on its degree, a polynomial can be called as linear polynomial, quadratic polynomial, cubic polynomial and so on.

The polynomial with all the coefficients as zeros is called a zero polynomial.

A polynomial with a single term of a real number is called a constant polynomial.

A polynomial of degree one is called a first-degree or linear polynomial. The general form of a linear polynomial is ax + b, where a and b are real numbers and a â‰ 0.

A polynomial of degree two is called a second degree or quadratic polynomial. The general form of a quadratic polynomial is ax

A polynomial of degree three is called a third-degree or cubic polynomial. The general form of a cubic polynomial is ax

A polynomial of degree four is called a fourth-degree or biquadratic polynomial. The general form of a quadratic polynomial is ax

The value of a polynomial p(x) when x = k (k is a real number) is the value obtained by substituting x as k. It is denoted by p(k).

The zero of the polynomial is defined as any real value of x, for which the value of the polynomial becomes zero.

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

The zero of the polynomial is the x-coordinate of the point, where the graph intersects the x-axis. If a polynomial p(x) intersects the x-axis at ( k, 0), then k is the zero of the polynomial.

The graph of a linear polynomial intersects the x-axis at a maximum of one point. Therefore, a linear polynomial has a maximum of one zero.

The graph of a quadratic polynomial intersects the x-axis at a maximum of two points. Therefore, a quadratic polynomial can have a maximum of two zeroes. In this case the shape of the graph is a parabola. The shape of the parabola of a quadratic polynomial ax^{2} + bx + c, a â‰ 0 depends on a.

If a > 0, then the parabola opens upwards.

If a < 0, then the parabola opens downwards.

Geometrically a quadratic polynomial can have either two distinct zeroes or two equal zeroes or no zero. This indicates that a quadratic polynomial has almost 2 zeroes.

The graph of a cubic polynomial intersects the x-axis at maximum of three points. A cubic polynomial has a maximum of three zeroes.

In general, an n^{th}-degree polynomial intersects the x-axis at a maximum of n points. Therefore, an n^{th}-degree polynomial has a maximum of n zeroes.