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Home >> Polynomials >> Factoring of Quadratic Polynomials >> Factoring Quadratic Polynomials by Splitting Middle Term >>

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
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