Factoring each expression?

1.
y^2 - 8y + 15

Think of two numbers whose sum is -8 and product 15. They are -3 and -5

So write (y - 3)(y - 5)

2.
For the next one a little help, the factors are 8 and 4

3.
-x^2 + 9x - 18
Do not fear '-x^2'. Think of two numbers whose product is 18 (-1 from -x^2 times -18 gives 18) and sum is 9. They are 6 and 3. Now replace +9x with +6x + 3x and factor. See

-x^2 + 6x + 3x - 18

-x(x - 6) + 3(x - 6)

(-x + 3)(x - 6) OR (3 - x)(x - 6) OR -1(x - 3)(x - 6)

Let's try the next one

4.
-1 * -35 = 35. Now find two numbers whose product is 35 and sum is 12. They are 7 and 5. Now write

-w^2 + 7w + 5w - 35

-w(w - 7) + 5(w - 7)

(-w + 5)(w - 7)

OR

(5 - w)(w - 7)

OR

-1(w - 5)(w - 7)

y^2 - 8y + 15 = (y - 3)(y - 5) answer//
x^2 - 12x + 32 = (x - 4)(x - 8) answer//
- x^2 + 9x - 18
= - (x^2 - 9x + 18)
= - (x - 3)(x - 6) answer//

- w^2 + 12w - 35
= - (w^2 - 12w + 35)
= - (w - 5)(w - 7) answer//

y^2-8y+15
=y^2-5y-3y+15
=y(y-5)-3(y-5)
=(y-5)(y-3)

-w^2+12w-35
=-w^2+7w+5w-35
=w(-w+7)-5(-w+7)
=(-w+7)(w-5)

1y² - 8y + 15
Factor pairs of (1×15): ±(1 and 15), ±(3 and 5)
-3 + -5 = -8
y² - 8y + 15 = (y - 3)(y - 5)