Question

Question 3Factor the polynomial.16x^2+40x + 25

Answer 1

$16x^2+40x+25$

To factorize the given function you:

You can find if the equation correspond to a perfect square trinomial by knowing that the numbers 16x^2 and 25 are perfect squares (numbers that have a perfect sqare root) and the term 40x is equal to 2 times 4x*5. and 5.

Then,

$\begin{gathered} 16x^2=(4x)^2 \\ 25=5^2 \\ 40x=2(4x)^{}(5) \end{gathered}$

The equation follows the next general form to a perfect square trinomial:

$a^2+2ab+b^2$

Then, you can rewrite the given equation as:

$(4x)^2+2(5)(4x)+5^2$

And knowing that:

$a^2+2ab+b^2=(a+b)^2$

You get that the given equation is equal to:

$(4x+5)^2$