Hi,
we can see from the statement that two terms containing x, x^2 will always be positive and -10x will be positive if x is -ive..
so the equation will have greatest value if x is -ive, and lower the value of x, greater is the equation.
so -4 will give the greatest value..

second way could be to factorize it..
x^2 − 10x + 16 = (x-8)(x-2)...
(x-8)(x-2) will have greatest value when x will be -ive as both terms will be -ive and the product would give us a positive value..
ans A
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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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IMO

x^2 − 10x + 16
= x^2 − 10x + 25 – 9
=(x-5)^2 – 9

=>( x^2 − 10x + 16)max
<=> (x-5)^2 max
<=> x = -4
*with value of x between − 4 and 4, inclusive

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??

Let’s first factor the given quadratic.

x^2 − 10x + 16

(x - 8)(x - 2)

In order to make the expression the greatest, we need (x - 8) and (x - 2) to be either both positive or both negative.

Looking at the answer choices, we see that when x is -4, we have the largest possible product:

-12 x -6 = 96

Answer: A
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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

Put the options values in the quadratic and try you will get maximum value.

remember square of negative no. always positive and multiplication of negative numbers always positive.

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