Question

The tiles show a factorization of 4x^2+6x+2. Write the factorization shown by the tiles.

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Answer 1

2(x + 1)(2x + 1)

Explanation:

`y = 2(2x^2 + 3x + 1)`

Factor the trinomial in parentheses.

Since a - b + c = 0, use shortcut. One real root is -1 and the factor is (x + 1). The other root is:
`(-c)/(a)= -1/2`

and the factor is
`(x+(1)/(2))`

Factor form of y:

y = 2(x + 1)(2x + 1)

Answer 2

(2x +1)(2x +2)

Explanation:

One factor is the sum of the tiles across the top of the figure: x+x+1 = 2x+1.

The other factor is the sum of the tiles down the left side of the figure: x+x+1+1 = 2x+2.

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The factorization shown by the tiles is ...

4x^2 +6x +2 = (2x +1)(2x +2)