Note: General forms:
1) Linear polynomial : ax + b
2) Quadratic polynomial : ax2 + bx + c
3) Cubic polynomial : ax3 + bx2 + cx + d , a, b, c, d are reals and a ¹ 0.
Equality of polynomials :
i.e. coefficients of like powers of x are equal.
Multiplication of a polynomial by real numbers :
If k is any real number and is any polynomial then
For example,
Sum and difference :
Example
If p (x) = x3 + 5x2 - 2x - 1 and q (x) = x2
- 8x + 1 then find :
1) p ( x ) + q ( x )
2) p ( x ) - q ( x )
3) 2 p ( x ) - 3 q ( x )
Solution:
Note : Degree of the product p (m) ´
q (m) = degree of p (m) + degree of q (m), i.e. 2 + 1 =
3
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