Question

factor the following trinomial. 25x² - 40x + 16 (?x - )²

Explanation:

Step1: Recall the perfect square trinomial formula

The perfect square trinomial formula is \((a - b)^2=a^{2}-2ab + b^{2}\). We need to match \(25x^{2}-40x + 16\) with this form.

Step2: Identify \(a\) and \(b\)

For the first term \(25x^{2}=(ax)^{2}\), so \(a^{2}=25x^{2}\), then \(a = 5x\) (since we are dealing with the form \((ax - b)^2\)).
For the last term \(16=b^{2}\), so \(b = 4\) (since the middle term is negative, we take the positive square root for \(b\) as the sign in the binomial is negative).
Now check the middle term: \(-2ab=-2\times(5x)\times4=-40x\), which matches the middle term of the given trinomial.
So \(25x^{2}-40x + 16=(5x - 4)^{2}\).

Answer:

The first box (for the coefficient of \(x\)) is \(5\) and the second box (the constant term) is \(4\), so the factored form is \((5x - 4)^{2}\), with the values in the boxes being \(5\) and \(4\) respectively.