In this session we are going to discuss the polynomial factorizing. When we think about factorizing then only one thing comes in our mind that factorizing of numbers. The factorizing polynomial is not same as factorizing of numbers but the way of factorizing of both are similar. In the method of factorizing we find the number which divides the given original numbers evenly. But this condition is not applicable for polynomial factorizing. When we factorizing the polynomial we divide the numbers or given variables out of the given expression. Factoring polynomial is just inverse of multiplying polynomials. When we doing simple factorizing we find a prime factors which multiplying both sides and give a number. Let’s take an example, 8 = 2 × 4 , or 16 = 2 × 2 × 4.
From the above example, similarly we factoring the polynomial. In case of polynomial, when we factorizing polynomial we find the simple polynomial, and then we multiply both sides by that simpler polynomial which provide the starting polynomial. In polynomial factorizing generally we break the given equation into polynomials and these polynomials having constants and coefficients. Now we are knowing that how to factor polynomials. There are some formulas which help us for finding the polynomial factorizing and these are given below;
If there is any common factor then we apply the formula, m(a) + m (b)= m (a + b).
If there are several common factor then the formula is, m a + m b + n a + n b = m(a + b) + n(a + b) = (m + n ) (a + b).
If there is two squares terms then the formula is a2 – b2 = (a + b)(a – b).
If there is two cubes terms then the formula for sum is a3 + b3 = (a+ b)(a2 – a b + b2).
If there is two cubes terms then the formula for difference is a3 – b3 = (a- b)(a2 + a b + b2).
The formula for perfect square is m2 + 2mn + n2 = (m + n)2.
The formula for perfect cube is m3 + 3m2 n + 3mn2 + n3 = (m + n)3.
The simple or most basic type of factoring is difference of two squares. Now here we want to know how to we factor that square term and this is necessary for polynomial factorizing if we want to know how to factor polynomials. We take an example which shows the factoring of difference of two squares. We have a equation that is,
In above given equation a2 is a square because it is equal to e *a and 9 is also a square because it is equal to 3 * 3.