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The model represents the factorization of 2x2+5x+3. An algebra tile configuration. 4 tiles are in the factor 1 spot: 2 +x tiles, 2 + tiles. 2 tiles are in the factor 2 spot. : 1 +x tile, 1 + tile. 10 tiles are in the product spot in 4 columns with 2 rows. First row: 2 + x squared tiles, 3 + x tiles. Second row: 2 + x tiles, 3 + tiles. What are the factors of the polynomial?.



Answer :

Required factors for the given polynomial 2x² + 5x + 3 is given by

(2x + 3) ( x+ 1).

As given in the question,

Given polynomial is equal to :

2x² + 5x + 3

Simplify the given polynomial by factorizing it:

2x² + 5x + 3

Standard form of quadratic equation is:

ax² + bx + c

Factors of the equation 2x² + 5x + 3  are:

x = (-b ± √b² -4ac )/2a

x = ( -5 ± √5² -4(2)(3) )/2(2)

   = (-5 ± 1) /4

⇒(2x +3) (x+1) are the factors

Therefore, the required factors of the given polynomial is given by       ( 2x + 3 ) ( x + 1 ).

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