For what value of x between − 4 and 4, inclusive, is the value of x^2 − 10x + 16 the greatest?

(A) − 4
(B) − 2
(C) 0
(D) 2
(E) 4
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x^2 − 10x + 16
=x^2 - 8x - 2x + 16
=x(x-8) -2(x-8)
= (x-2)(x-8)
Now we can substitute the values of x
x=-4 , then (-6)*(-12) = 72
x=-2 , then (-4)*(-10)= 40
x= 0 , then (-2)*(-8) = 16
x=-2 , then 0* - 8 = 0
x=4 then 2* - 4 = -8

Answer A

Alternatively we can analyse the original expression x^2 − 10x + 16
The term x^2 will be always positive or zero(when x=0)
So value of x^2 will increase as value of x increases .
To maximize -10x , we need the smallest negative value of x in the range [-4,4] . Thus , -4 should give us that max value for -10x .

Answer A
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So here we can just substitute the values from the options and check for which one does the value of x the greatest. But why is the method in the official guide showing all the values from -4 to 4 inclusive and then finding out the greatest value .Isn't that method simply lengthy??

It tells us the numbers between -4 and 4 inclusive.

From the question stem we have \(x^2 -10x + 16\)

\(x^2\) will always be positive

-10x, if x is negative will provide a positive integer.

From the above we can just directly substitute in the equation with -4 giving the greatest value.

Answer choice A