Question

How do you factor `k^2 + 8k = 84`?

Answer 1

`(k-6)(k+14)=0`

Explanation:

One way to approach this problem is by "completing the square"

`k^2+8k =84`
`color(white)("XXXX")`if `k^2+8x` are the first 2 terms of a squared binomial)
`color(white)("XXXX")` `rarr` the third terms must be `(8/2)^2`

`k^2+8k+4^2 = 84 + 4^2`

`(k+4)^2 = 100`

`k+4 = +-10`

`k= 6 or k=-14`

`(k-6)(k+14) = 0`

Answer 2

Factor: y = k^2 + 8k - 84

Ans: (k - 6)(k + 14)

Explanation:

`y = k^2 + 8k - 84.`
I use the new AC Method. a and c have opposite signs.
Factor pairs of (-84) --> (-2, 42)(-3, 28)(-6, 14). This sum is 8 = b.

y = (k - 6)(k + 14)