Question

Honestly if anyone could help be understand how to solve these by factoring, that would be great! Thank you!

Answer 1

1) Option 3

2) Option 3

3) Option 3

4) Option 1

5) Option 2

6) Option 3

7) Option 1

Explanation:

1)
`y = x^2 + 4x + 3`

Lets split the middle term.

`=> y = x^2 + 3x + x + 3`

`=> y = x(x+3) + 1(x + 3)`

`=> y = (x+1)(x+3)`

∴
`x = -3 , -1`

2)
`y = 8x^2 - 22x + 5`

Lets split the middle term.

`=> y = 8x^2 - 20x - 2x + 5`

`=> y = 4x(2x - 5) - 1(2x - 5)`

`=> y = (2x - 5)(4x - 1)`

∴
`x =(1)/(4) , (5)/(2)`

3)
`y = x^2 - 5x`

`=> y = x(x - 5)`

∴
`x = 0 , 5`

4)
`y = 12x^2 + 18x`

`=> y = 6x(2x + 3)`

∴
`x = (-3)/(2) , 0`

5)
`y = x^2 - 7x + 12`

Lets split the middle term.

`=> y = x^2 -3x - 4x + 12`

`=> y = x(x - 3) - 4(x - 3)`

`=> y = (x - 3)(x - 4)`

∴
`x = 3,4`

6)
`y = 3x^2 + 10x + 8`

Lets split the middle term.

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

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

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

∴
`x = -2 , (-4)/(3)`

7)
`y = x^2 - 4x - 45`

Lets split the middle term.

`=> y = x^2 - 9x + 5x - 45`

`=> y = x(x - 9) + 5(x - 9)`

`=> y = (x - 9)(x + 5)`

∴
`x = -5 , 9`