I am trying to factor the expression -8y^2+28y-60 but can't get an answer that is correct.
Here is an example of how the problem is supposed to be factored. If you have 21x2-77x-28 the first thing you would do is (21x )(x ). Next you would find two numbers that multiplied into -28. After this your work would look like this (21x+7)(x-4). Now you would multiply 21x and -4 to get -84x and you would multiply 7 and x to get 7x. After that you add -84x and 7x to get the middle number in the expression which is -77x.
Could someone please show me how to factor -8y^2+28y-60?
-8y^2+28y-60
-4(2y^2 - 7y + 15)
The discriminant is 49-120 which is negative, so there are no real factors.
To factor the expression -8y^2 + 28y - 60, we can follow a similar process as the example you provided.
Step 1: Look for common factors (if any)
In this case, there are no common factors among -8, 28, and -60.
Step 2: Write the expression in the form ( )( )
To start factoring, we write the expression as ( -8y )( y ).
Step 3: Find two numbers that multiply to give the product of the coefficient of y^2 term (-8y^2) and the constant term (-60).
The product of -8y^2 and -60 is 480y^2.
Let's find two numbers whose product is 480 and can combine to give 28y when one is multiplied by -8y and the other by y.
One possible pair of numbers is 6 and 80 because 6 * 80 equals 480, and 6 + 80 equals 86.
Step 4: Rewrite the expression by splitting the middle term
Replace the middle term (28y) with the sum of the two numbers we found (6 and 80).
-8y^2 + 6y + 80y - 60
Now, group the terms in pairs:
(-8y^2 + 6y) + (80y - 60)
Step 5: Factor out the greatest common factor (GCF) from each group
From the first group, we can factor out 2y: 2y(-4y + 3)
From the second group, we can factor out 20: 20(4y - 3)
Step 6: Combine the factored groups
Putting it all together, we have:
2y(-4y + 3) + 20(4y - 3)
Step 7: Factor out the greatest common factor (GCF) from the entire expression
Now, we can factor out the common factor of -2 from both terms:
-2(2y(-4y + 3) + 10(4y - 3))
Simplifying further:
-2(-8y^2 + 6y + 40y - 30)
Step 8: Combine like terms
-2(-8y^2 + 46y - 30)
This is the factored form of the expression -8y^2 + 28y - 60:
-2(-8y^2 + 46y - 30)
Note: It's essential to remember that factoring may not always be possible or straightforward for every expression. In some cases, factoring may not be the most efficient method, and alternative approaches like the quadratic formula may be used.