**Degree of the polynomial**

**The highest power of x in p(x) is called the degree of the polynomial.**

__Polynomial__** of degree 1 is known as linear polynomial.**

**Standard form is ax+b, where a and b are real numbers and a ≠ 0.**

**4x+1 is a linear polynomial. **

**Polynomial of degree 2 is known as quadratic polynomial.**

**Standard form is ax**^{2}** + bx + c, where a, b and c are real numbers and a ≠ 0**

**x**^{2}** + 4x + 6 is an example for quadratic polynomial.**

**Polynomial of degree 3 is known as cubic polynomial.**

**Standard form is ax**^{3}** + bx**^{2}** + cx + d, where a, b, c and d are real numbers and a ≠ 0.**

**x**^{3}** + 2x + 6 is an example for cubic polynomial.**

**If p(x) is a polynomial in x, and if k is any real number, then the value obtained by**

**replacing x by k in p(x), is called the value of p(x) at x = k, and is denoted by p(k).**

**p(x) = x**^{3}** + 4x + 5**

**at x = -1 we have**

**p(-1) = (-1)**^{3}** + 4(-1) + 5**

**= -1 - 4 + 5**

**= 0**

**As p(–1) = 0, –1 is called the zeroes of the quadratic polynomial x**^{3}** + 4x + 5. More generally, a real number k is said to be a zero of a polynomial p(x), if p(k) = 0 the zeroes of a quadratic polynomial ax**^{2}** + bx + c, a ≠ 0, are precisely the x-coordinates of the points where the parabola representing y = ax**^{2}** + bx + c intersects the x-axis.**

**In general, given a polynomial p(x) of degree n, the graph of y = p(x) intersects the x- axis at atmost n points. Therefore, a polynomial p(x) of degree n has at most n zeroes.**

**If α and β are zeros of the polynomial then**

**Sum of its zeroes α + β**

**= -(Coefficient of x)/(Coefficient of x**^{2}**) = -b/a**

**Product of zeroes = αβ**

**Constant term/Coefficient of x**^{2}** = c/a**

**If α, β, γ are the zeroes of the cubic polynomial ax3 + bx2 + cx + d, then**

**α + β + γ = -b/a**

**αβ + αγ + βγ = c/a**

**αβγ = -d/a**

**Division Algorithm**

**If p(x) and g(x) are any two polynomials with g(x) ≠ 0, then we can find polynomials q(x) and r(x) such that**

**p(x) = g(x) * q(x) + r(x)**

**where r(x) = 0 or degree of r(x) < degree of g(x).**

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