Question

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

Answer 1

Answer:

$(y+3)(y-5)$

Step-by-step 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.

$y^2-2y-15$
$(y^2+3y)+(-5y-15)$
$y^2=yy=y(y+3)$
$y(y+3)+(-5y-15)$
$(-5y-15)=-5(y-15)$
$y(y+3)+-5(y-15)$
$15\div5=3$
$y\left(y+3\right)-5\left(y+3\right)$
$y\left(y+3\right)-5\left(y+3\right)=(y+3)(y-5)$
$=(y+3)(y-5)$

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

Hope this helps.

Answer 2

Answer:

$(y-5)(y+3)$

Step-by-step 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 $(y-5)$:

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