Question

Determine the factors of 5x2 + 29x _ 6

Answer 1

The factors of given equation
`5x^2+29x-6` is
`(5x-1)(x+6)`

Explanation:

Given equation
`5x^2+29x-6`

We have to determine the factors of given equation.

Quadratic equation is an equation with highest degree 2.

Consider the given quadratic equation
`5x^2+29x-6`

We can solve the quadratic equation
`5x^2+29x-6` using middle term splitting method.

splitting middle term can be done by writing middle term in such a way that the product of coefficient is the product of remaining two terms.

29x can be written as 30x-1x

`\Rightarrow 5x^2+29x-6`

`\Rightarrow 5x^2+30x-x-6`

Taking 5x common from first two terms and -1 from last two terms , we have,

`\Rightarrow 5x(x+6)-1(x+6)`

`5x^2+29x-6=(5x-1)(x+6)`

Thus, the factors of given equation
`5x^2+29x-6` is
`(5x-1)(x+6)`

Answer 2

The answer is (x + 6)(5x - 1).

5x² + 29x - 6 = 5x² + 30x - x - 6 =
= (5x · x + 5x · 6) - (x + 6) =
= 5x(x + 6) - 1(x + 6) =
= (x + 6)(5x - 1)