Question

How do you write `y= 4x^2 + 11x + 6` in factored form?

Answer 1

y = `(x + 2)(4x + 3)`

Explanation:

Their are several methods to factorize polynomials. Here I have used splitting the middle term method.

In this we split the middle term into two terms making the polynomial easily factorizable.

The spiting should be done such that the product of the two middle terms should be equal to the product of coefficients of the `x^2` and constant term.

`y = 4x^2 +11x + 6`

Terms would be `8` and `3` as `8 xx 3 = 4 xx 6`

`y = 4x^2 + 8x + 3x + 6` or `y = 4x^2 + 3x + 8x + 6`

`y = 4x(x+2) + 3(x+2)` or `y = x(4x +3) + 2(4x + 3)`

Taking common terms

• `(x+2)`
• `(4x +3)`

`y = (4x +3)(x + 2)` or `y = (x+2)(4x+3)`

Which is the same answer.