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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