Question

Hello people ~
factorise: y² - 2y - 15​

Answer 1

`(y+3)(y-5)`

Explanation:

Given the following equation:


`y^2-2y-15`

To factor any equation, we must first break the equation into different groups and then factor out common terms in till we reach our solution.


`y^2-2y-15`

`(y^2+3y)+(-5y-15)`

`y^2=yy=y(y+3)`

`y(y+3)+(-5y-15)`

`(-5y-15)=-5(y-15)`

`y(y+3)+-5(y-15)`

`15/5=3`

`y\left(y+3\right)-5\left(y+3\right)`

`y\left(y+3\right)-5\left(y+3\right)=(y+3)(y-5)`

`=(y+3)(y-5)`

Your answer is "(y + 3)(y - 5)."

Hope this helps.

Answer 2

`(y-5)(y+3)`

Explanation:

To factorize
`y^2-2y-15`

`\textsf{for} \ ax^2+bx+c \ \textsf{find} \ v, w \ \textsf{such that} \ v \cdot w=a \cdot c \ \textsf{and} \ v+w=b\\ \textsf{ and group into} \ (ax^2+vx)+(wx+c)`

`a \cdot c=1 \cdot -15=-15`

`b=-2`

Therefore, the 2 numbers that multiply together to give -15 and add together to give -2 are: -5 and 3

`\implies y^2-5y+3y-15`

`\implies (y^2-5y)+(3y-15)`

Factor the parentheses:

`\implies y(y-5)+3(y-5)`

Factor out the common term
`(y-5)`:

`\implies (y-5)(y+3)`