2. Quadratic factorization using splitting of middle term

Factorize ${6x}^2 + 19x + 10$.

To form the factor: ${\mathit{ax}}^2 + \mathit{bx} + c$ where (\(a = 6\), \(b = 19\) and \(c = 10\)).

 

Step 1: Find the product of the first and last term \((a × c)\).

 

$6\times 10 = 60$.

Step 2: Find the factors of \(60\) using the middle term in such a way that the addition or subtraction of that factors \((19x)\) (Splitting of the middle term).

 

$15\times 4 = 60$ and $15 + 4 = 19$.

Step 3: Write the middle term using the sum of the \(2\) new factors, including the correct signs.

 

Step 4: Group the terms to make pairs using the first two terms and also the last two terms. Factor each pair by finding common factors.

 

Step 5: Factor out the common factors from the term.

 

 

The factors of ${6x}^2 + 19x + 10$ is $(3x + 2)\; ( 2x + 5)$.