Question

Hello people ~
factorise: y² + 4y - 21​

Answer 1

`(y+7)(y-3)`

Explanation:

To factorize
`y^2+4y-21`

`\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 -21=-21`

`b=4`

Therefore, the 2 numbers that multiply together to give -21 and add together to give 4 are: 7 and -3

`\implies y^2+7y-3y-21`

`\implies (y^2+7y)+(-3y-21)`

Factor the parentheses:

`\implies y(y+7)-3(y+7)`

Factor out the common term
`(y+7)`:

`\implies (y+7)(y-3)`