An algebraic expression is an expression which contains constants, operations etc. For example ax + by – c =0 is a simple algebraic expression.
Polynomials are generally represented as an + an-1 + an-2 +……. + c = 0 and following are the factoring polynomial problems,
Problem:
(x + 1) (x+ 4) ( x + 3)
(x + 1) (x+ 4) = x2 + 4x + x + 4 = x2 + 5x + 4
(x2 + 5x + 4) (x + 3) = x3 + 3x2 + 5x2 +15x +4x + 12 => x3 + 8x2 + 19x + 12 = 0
Rational expressions are type of algebraic expressions which are represented in form of a fraction i.e. as shown below,
(x + 1) / (x + 2) or (x2+x+1) / (x +1)2 etc
Functions and relations are the other major important in algebra, a function is also said to be an algebraic expression expressed as f(x). And the relations are made between an input and output based up on its functionalities.
f(x) : x3 + 8x2 + 19x + 12 = 0 is a function.
Solved Problems
The following problems show how to factor polynomials
1) Find the factors for x2 + 2x + - 8 = 0
1 x 8 = 8
4 – 2 = 2; 4 x2 = 8
So the above equation can be written as
x2 + 4x – 2x – 8 = 0
x (x + 4) – 2(x + 4) =0
(x – 2) (x + 4) = 0
x = 2 and x = -4 are the factors.
2) Find the factors for function f(x): 3x2 + 11x – 4
3 x 4 = 12
12 – 1 = 11(since 11 is b)
3x2 + 12x – x - 4 = 0
3x (x + 4) -1 (x + 4)
So the factors are (3x – 1) and (x + 4).
3) Find the factors for 2x2 + 4x – 6 = 0
2x2 can be factored as (2x) (x), and 4 can be written as (6 - 2)
2x2 + 4x - 6 = 0
2x2 + 6x – 2x - 6= 0
2x(x + 3) -2(x + 3) = 0
(2x – 2) (x + 3) = 0
x = 1 and x = -3 are the factors.
4) Find the factors for 2x2 + 10x – 8 = 0
2 x 8 = 16
8 + 2 = 10 (since 10 is b)
2x2 + 8x + 2x – 8 = 0
2x (x + 4) -2 (x + 4)
So the factors are (2x – 1) and (x + 4).
Related Tags
Solved examples of Polynomial Problems , Polynomial solved problems , Explain Polynomial Problems