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

User Ratique
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1 Answer

17 votes
17 votes

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

User Tomy
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