Question

What is the binomial to the factor of `14a^2 - 15a + 4`?

Answer 1

`14a^2-15a+4 = (2a-1)(7a-4)`

Explanation:

We can factor the given quadratic as a product of binomials using an AC method:

First find a pair of factors of `AC = 14 * 4 = 56` with sum `B=15`

The pair `8, 7` works in that `8*7 = 56` and `8+7=15`

Use this pair to split the middle term and factor by grouping:

`14a^2-15a+4 = (14a^2-8a) - (7a-4)`

`color(white)(14a^2-15a+4) = 2a(7a-4) - 1(7a-4)`

`color(white)(14a^2-15a+4) = (2a-1)(7a-4)`