The factorization of x2 + 5x + 6 is modeled with algebra tiles below. what are the factors of the trinomial?

Given: Trinomial is x² + 5x + 6

To find: Factors of given Trinomial

factors of Trinomial can be found using identity or using middle term split method.

In given Trinomial no other than x² is a square term. ⇒ we cant use identities.

So we factories given trinomial by middle term split

Consider,

x² + 5x + 6

Split 5x in 3x and 2x

⇒ x² + 3x + 2x  + 6  

Taken x common from first 2 terms and 2 from last 2 terms.

⇒ x( x + 3 ) + 2 ( x + 3 )  

By Grouping ( x+3 ) &  ( x+2 ), we get

⇒ ( x + 3 )( x +  2 )

Factors of given Trinomial = ( x + 3 )( x +  2 )

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