Question

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

Answer 1

Answer:

$(y+7)(y-3)$

Step-by-step 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 $(y+7)$:

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