Question

An x-method chart shows the product a c at the top of x and b at the bottom of x. Below the chart is the expression a x squared + b x + c. What are the factors of x2 – 144? And

Answer 1

✔ (x – 12)

and

✔ (x + 12)

Explanation:

Answer 2

`(x -12)(x + 12)`

Explanation:

Given

See attachment for chart

Required

The factors of
`x^2 - 144`

First, express
`x^2 - 144` as
`ax^2 + bx + c`

So, we have:

`x^2 - 144 = x^2 + 0x - 144`

Compare the above expression to:
`ax^2 + bx + c`

We have:

`ax^2 + bx + c = x^2 + 0x - 144`

So:

`a =1`

`b =0`

`c = -144`

and

`a * c = d * e`

Calculate ac

`a* c = 1 * -144`

`a* c = -144`

Rewrite as:

`a* c = -12 * 12`

Recall that:

`a * c = d * e`

Hence:

`d = -12; e = 12`

So, on the x chart, we have:

ac

d e

b

This gives:

-144

-12 12

0

The factors are

`(x + d)(x + e)`

`(x -12)(x + 12)`