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## 02 POLYNOMIALS

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

Linear polynomial:The polynomial with degree  1.

Quadratic polynomial:The polynomial with degree  2.

Cubic polynomial:The polynomial with degree 3 .

Value of polynomial: Value obtained by replacing by some real number k , is  value of polynomial at                            x=k   .It is denoted by .

value of p(x) at  x=-2 =p (-2) =5

for some k ,Kis called zero or root of polynomial.

Geometrical meaning of zero:

$p\left(–b/a\right)=a\left(–b/a\right)+b=0$

So, we say linear polynomial p(x)  has only one   zero, and it is the point where its graph cuts x axis

$p\left(x\right)=a{x}^{2}+bx+c$

Case 1):a>0 ,.   graphis upward parabola .

Graph cuts  x axis at 2 points or point or may not cut x axis.

Case 2  :a<0,The graph is downward parabola.

Graph cuts  axis at  points or  point or may not cut x axis.

In either cases i) If the graph cuts x axis in two points, then we say polynomial has 2 zeroes.

1. ii) If the graph cuts x axis in only one point, then we say polynomial has 1 zero.

iii) If the graph does not cut x axis, then we say zeroes of polynomial do not exist.

Relation between zeroes and coefficients of polynomial:

Division algorithm for polynomial:

Or we can express polynomial as