Factor completely 2 ay 2 + 5ay - 3a O-a(2y - 1)(y - 3) O a(2y - 3)(y + 1) a(2y - 1)(y - 3) please and thank you

a(2y - 1)(y + 3)

Step-by-step explanation:

Factor the following:

2ay² + 5ay - 3a

Factor a out of 2ay² + 5ay - 3a:

a(2y² + 5y - 3)

The coefficient of y² is 2 and the constant term is -3. The product of 2 and -3 is -6. The factors of -6 which sum to 5 are -1 and 6.

So,

a(2y² + (6 - 1)y - 3)

a(2y² + 6y - y - 3)

a(2y(y + 3) - 1(y + 3))

Factor y + 3 from 2y(y + 3) - 1(y + 3):

a(2y - 1)(y + 3)

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²