Factor the polynomial 4x^2 + 12 + 9

Ymartin asked Jun 23, 2022

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12 votes

Factor the polynomial
4x^2 + 12 + 9

Ymartin asked Jun 23, 2022

2.4k points

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12 votes

Answer:

The answer is
(2x+3)^2 .

Explanation:

Multiply the coefficient of the squared term and the constant. Then, find the factors that add up to 12:

$4*9=36\\36:\{1*36,2*18,3*12,4*9,6*6\}\\6+6=12$

Split the middle term:

4x^2+6x+6x+9

Factor by grouping:

$[4x^2+6x]+[6x+9]\\2x(2x+3)+3(2x+3)\\(2x+3)(2x+3)\\(2x+3)^2$

Matthiasdv answered Jun 28, 2022

2.5k points

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