One of the factors of (3x^2 −16x + k) is (x − 7). Determine the value of k.

Question

anonymous · Answer

1. You know that the second expression that multiplies '(x-7)' must have a 3x because if it didn't you would not be able to obtain 3x^2 therefore,

anonymous · Answer

$$(x-7)(3x+n)= 3x^2+xn-21x-7n$$

anonymous · Answer

Now the original equation was $$3x^2-16x+k$$
now setting that equal to the new equation, $$3x^2+xn-21x-7n=3x^2-16x+k \rightarrow xn-21x = -16x \rightarrow n = 5$$

since n = 5 $$-7n \rightarrow -7(5) = -35$$ , k = -35

hartnn · Answer

if x-7 is a factor,
then x =7 is one of the root of the equation 3x^2 −16x + k = 0 ! 

so, x= 7 satisfies that equation.
just plug in x=7 in that and find k :)

anonymous · Answer

Refer to the attachment from Mathematica 9.