In mathematics, any expressions which consist of constants, variables and exponent values that are joined together by mathematical operators like addition, subtraction, multiplication, are said to be Polynomials. Exponent’s values can be 0, 1, 2, 3 and 4 ….etc. Infinite values are not possible in case of polynomials expression. For example: 7xy2 – 5x + 5y3 – 15, this given equation is polynomial equation, in this equation exponents values are 0, 1, 2 and 3. Polynomial expression can also have negative and fraction values. It means negative and fraction values are also present in case of polynomial expression. It cannot be joined by division operator.
Now we will see how to solve Factoring Polynomials. Polynomial expressions can be factored by two methods i.e. direct method and by quadratic method. Here we will see quadratic to solve polynomial expressions.
Suppose we have a polynomial expression p2 + p – 4, we can factorize this polynomial as shown below:
We will find its factor by Quadratic Formula. Formula to find factors is given by:
P = -b + √ (b2 - 4ac) / 2a, here value of 'a' is 1, value of 'b' is 1 and value of 'c' is -4. So put these values in formula. On putting these values we get:
P = - 1 + √ [(1)2 - 4(1) (-4)] / 2(1); on moving ahead we get:
P = - 1 + √ (1 + 16) / 2, we can also write it as:
P = - 1 + √ (17) / 2. So here we get two factor of this expression, one positive and other negative.
P = -1 + √ (17) / 2 and P = -1 - √ (17) / 2.
These two are factors of above expression. Using this formula we can find factors of any polynomial expression.