Question

How do you factor `7x^2-30x+27`?

Answer 1

(7x-9)(x-3)

Explanation:

Multiply 7x27 and find a combination of factors of 7x27, such that their sum or difference is -30. This method is called splitting the middle term.

In the present case 7x27can be factorised as 21x9.or (-21)x(-9). The sum of these factors is -30. Now we split the middle term:

`7x^2 -21x--9x +27`

Now make pairs and factorise,
7x(x-3) -9(x-3)

(7x-9)(x-3)

Answer 2

y = (7x - 9)(x - 3)

Explanation:

Use the new AC Method to factor trinomials (Google Search)
`y = 7x^2 - 30x + 27 =` 7(x + p)(x + q)
Converted trinomial:
`y' = x^2 - 30x + 189 =` (x + p')(x + q')
Find 2 number p' and q' knowing sum (b = -30) and product
(ac = 189). They are: (- 9) and (- 21).
Back to y, we get `p = (p')/a = -9/7`, and `q = (q')/a = - 21/7 = - 3`
Factored form:
`y = 7(x - 9/7)(x - 3) = (7x - 9)(x - 3)`