Factoring of Quadratic Polynomials by Splitting Middle Term

Factoring Quadratic Polynomials by Splitting Middle Term

When we cannot square the first and last term of a given quadratic polynomial then we can factorize it by another method which is called splitting the middle term If our quadratic polynomial is like ax2 + bx + c then we will find two numbers, whose sum is b and when we multiply we get ac Let's take an example and try to understand it Example 1 : 4x2 + 12x + 5 Solution: We have to find two numbers, whose sum is 12 (middle term) and when multiplied (first and last term) i.e. 4 X 5 we get 20 So these two numbers are - 10 + 2 = 12 10 X 2 = 20 Now we put both 10 and 2 numbers in the middle term of 12x and we get ∴ 4x2 + 12x + 5 = 4x2 + 10x + 2x + 5 or 2x(2x + 5) + 1(2x + 5) or (2x + 5)(2x + 1) Example 2 : 4x2 + 8x - 5 Solution: We have to find two numbers, whose sum is 8 (middle term) and when multiplied (first and last term) i.e. 4 X (-5) we get -20 So these two numbers are - 10 - 2 = 8 10 X (-2) = -20 Now we put both 10 and (-2) numbers in the middle term of 8x and we get ∴ 4x2 + 8x - 5 = 4x2 + 10x - 2x - 5 or 2x(2x + 5) - 1(2x + 5) or (2x + 5)(2x - 1) Example 3 : x2 + 14x + 45 Solution : We have to find two numbers, whose sum is 14 (middle term) and when multiplied (first and last term, x means it has value of 1) i.e. 1 X 45 we get 45 so these two are - 9 + 5 = 14 9 X 5 = 45 Now we put both 9 and 5 numbers in the middle term of 12x and we get ∴ x2 + 14x + 45 = x2 + 9x + 5x + 45 or x(x + 9) + 5(x + 9) or (x + 5) (x + 9) Study More Solved Questions / Examples Factorize 14y2 + 19y - 3 by splitting the middle term Factorize 24y2 -65y + 21 by splitting the middle term Factorize 5z2 - 16z - 21 by splitting the middle term