Luis Rojas

Luis Rojas

Answered question


Answer & Explanation



Skilled2023-05-29Added 488 answers

To determine the constant that should be added to the binomial x2+16x in order to make it a perfect square trinomial, we need to consider the square of a binomial pattern.
The square of the binomial (a+b)2 can be expanded as follows:
Comparing this pattern to the given binomial x2+16x, we can see that a2 corresponds to x2, 2ab corresponds to 16x, and b2 corresponds to the unknown constant we need to find.
From the comparison, we can deduce that 2ab=16x. In this case, a=x and b is the unknown constant we're looking for.
To find b, we can rewrite the equation as:
Substituting a=x:
Now, we can solve for b:
Therefore, the constant that needs to be added to the binomial x2+16x to make it a perfect square trinomial is 112.
Now, let's write and factor the trinomial.
The original binomial is x2+16x. To make it a perfect square trinomial, we add (112)2 to it:
Now, we can factor the trinomial:
And that's the factored form of the trinomial.

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