Question

Paul creates the diagram to help him factor 4x2 + x – 5 by using double grouping. His diagram is incomplete. Which terms should Paul write in squares M1 and M2? 5x and −4x –5x and 4x –2x and 10x 2x and −10x

Answer 1

5x and -4x

Explanation:

`4x^2 + x - 5`

`4x^2 + 1x - 5`

To find out factors we need to multiply 4 and -5 that is -20

Now product is -20 and sum is +1

We need to find out two factors whose product is -20 and sum is +1

5 times -4 = -20

5 + (-4) = +1

So +1x can be written as +5x - 4x

`4x^2 + 1x - 5` can be written as
`4x^2+5x - 4x- 5`

Answer 2

4x^2 + x - 5 = 4x^2 + 5x - 4x - 5

Therefore, required solution is 5x and -4x.