A method of factoring a trinomial by splitting the middle term of an expression or polynomial is called the factorization (or factorisation) by splitting the middle term.
An expression often appears with three terms in mathematics and it can be factored mathematically in some cases but the polynomial should have the following two properties.
You must study the following concept to understand the factorization of expressions or polynomials by splitting the middle term of trinomials.
The factoring of an expression that contains three terms can be done by the following steps.
Factorize the trinomial $x^2+6x+8$.
The given algebraic expression is already in descending order. So, need to do anything with the given polynomial.
Find the product of first and last terms of the expression.
$x^2 \times 8 \,=\, 8x^2$
Try to split the middle term $6x$ as two terms but their product should be equal to $8x^2$.
$2x+4x = 6x$ and $(2x)(4x) = 8x^2$.
$= \,\,\,$ $x^2+2x+4x+8$
Now, group the terms to factorize the algebraic expression by grouping.
$= \,\,\,$ $(x^2+2x)+(4x+8)$
$= \,\,\,$ $x(x+2)+4(x+2)$
$= \,\,\,$ $(x+2)(x+4)$
Therefore, the given trinomial $x^2+6x+8$ is factored as $(x+2)(x+4)$ by splitting the middle of the given expression.
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