Question

How do you factor `6r^2-28r+16`?

Answer 1

`6r^2-28r+16`

`=2(3r^2-14r+8)`

To factor `3r^2-14r+8` use a modified AC Method...

`A=3`, `B=14`, `C=8`

Look for a factorization of `AC=3xx8=24` into a pair of factors whose sum is `B=14`.

The pair `B1=2`, `B2=12` works.

Then for each of the combinations: `(A, B1)` and `(A, B2)`, divide by the HCF (highest common factor) to get the coefficients of a factor of `3r^2-14r+8` ...

`(3, 2)` (HCF `1`) `-> (3, 2) -> (3r-2)`
`(3, 12)` (HCF `3`) `-> (1, 4) -> (r - 4)`

So

`6r^2-28r+16 = 2(3r-2)(r-4)`

Answer 2

`2(3x-2)(x-4)`

Explanation:

Factoring requires a solid knowledge of the multiplication tables.

Always look for a common factor first - all these numbers are even.

`6r^2-28r +16 =2(3r^2-14r +8) " factor the trinomial"`

All the clues are in the trinomial o3 3 and 8. Compare the colors and read it as follows:

`color(orange)(3) color(blue)(-) color(red)(14) color(lime)(+) color(orange)(8)`

Find the factors of `color(orange)(3and 8)` which `color(lime)("ADD")` to give `color(red)(14)`

The signs will be `color(lime)("THE SAME")`, they are both`color(blue)(" minus")`

Use different factors of 3 and 8 and cross-multiply with different combinations, until the sum of the products is 14.

`color(white)(xxxx)color(orange)((3)" "(8))`
`color(white)(xxxxx) 3" "2 rarr 1xx2 =2`
`color(white)(xxxxx) 1" "4 rarr 3xx4 =ul12`
`color(white)(xxxxxxxxxxxxxxxxxx)14 larr "we have the correct factors"`

Now put the signs into the brackets.

`2(3x-2)(x-4)`