Question

factor the following trinomial. 36x² + 12x + 1 (?x + )²

Explanation:

Step1: Recall perfect square trinomial formula

A perfect square trinomial has the form \(a^{2}+2ab + b^{2}=(a + b)^{2}\). For the given trinomial \(36x^{2}+12x + 1\), we can rewrite \(36x^{2}\) as \((6x)^{2}\) and \(1\) as \(1^{2}\).

Step2: Check the middle term

Now, we check if the middle term \(12x\) is equal to \(2ab\) where \(a = 6x\) and \(b=1\). Calculating \(2ab\), we get \(2\times(6x)\times1 = 12x\), which matches the middle term of the trinomial.

Step3: Factor the trinomial

Using the perfect square trinomial formula, since \(a = 6x\) and \(b = 1\), the trinomial \(36x^{2}+12x + 1\) factors to \((6x + 1)^{2}\).

Answer:

The value in the green box (coefficient of \(x\)) is \(6\) and the value in the white box is \(1\). So the factored form is \((\boldsymbol{6}x+\boldsymbol{1})^{2}\).