Question

Given the following perfect square trinomial, fill in the missing term.

x2 − 16x + ____

Answer 1

Your Answer:

64

Step-by-step explanation:

Your answer would be 64 because the middle term of a perfect square trinomial must have the following:

• The first term must be a perfect square
• The last term must be a perfect square
• The middle term must be twice the product of the square roots of the first and last terms

All of these requirements are present in this trinomial. We already know that this is a perfect square trinomial because the question says it. All we need to find is the square root of the missing number that would give you 64 if multiplied by "x" and then "2". Since 8 · 2 = 16, we must find a number that has a square root of 8, in which this case, would be 64. So your final completed perfect square trinomial would be:
`x^(2) - 16x + 64`

Hope this helps y'all :D

Answer 2

The pattern is:
( a - b )² = a² - 2 a b + b² ( square of last term of binomial - the missing term)
x² - 2 · 8 · x + 8² = x² - 16 x + 64 = ( x - 8 )²
The missing term is: 64