y^2+4y-32=0 what is the greatest factor
(y+8)(y-4) = 0
I guess we can say that y+8 is the "greater" factor
To find the factors of a quadratic equation, we need to factorize it by breaking it down into two binomials. Let's solve the equation step by step:
The equation is: y^2 + 4y - 32 = 0
To factorize the equation, we need to find two numbers, let's call them A and B, such that their product is equal to the product of the square term (y^2) and the constant term (-32). In this case, the product of A and B should be -32.
Next, we need to find two numbers, A and B, such that their sum is equal to the coefficient of the middle term (4) in our equation. In this case, A + B should be equal to 4.
Let's find the factors of -32 that have a sum of 4:
-32 can be factorized as: -1 x 32, -2 x 16, -4 x 8
Out of these, -4 and 8 have a sum of 4.
Now, let's rewrite the middle term (4y) in the equation as the sum of -4y and 8y:
y^2 - 4y + 8y - 32 = 0
Now, let's split the equation into two groups, so we can factor by grouping:
(y^2 - 4y) + (8y - 32) = 0
Now, let's factor out the common terms from each group:
y(y - 4) + 8(y - 4) = 0
Now, we can see that we have a common factor of (y - 4) in each term, so we can factor it out:
(y - 4)(y + 8) = 0
Now, set each factor equal to zero:
y - 4 = 0 or y + 8 = 0
Solving for y in each equation, we get:
y = 4 or y = -8
So, the greatest factor of the equation y^2 + 4y - 32 = 0 is 4.