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