## anonymous one year ago One of the factors of (3x^2 −16x + k) is (x − 7). Determine the value of k.

1. anonymous

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,

2. anonymous

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

3. anonymous

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

4. hartnn

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 :)

5. anonymous

Refer to the attachment from Mathematica 9.