how do I start to solve this
3y^2+17y+20=
is your equation equal to zero?
if so then
3y^2+17y+20=0 factors to
(y + 4)(3y + 5) = 0
y = -4 or y = -5/3
It just says to factor
then just eliminate my last step
You must have learned a method to do this
so if I have this problem to factor 2x^2+7xy-30y I would do this to factor it x^2+xy+7+2-30y^2
you probably meant to type
2x^2+7xy-30y^2 or else it won't work
the method most students appear to use these days is the method of decomposition of the middle term.
In this method you multiply the first and last number coefficients ... 2*(-30) = -60
now look for two factors of -60 which have a sum of 7
after about 3 tries I got 12 and -5
so I will break up the middle term of 7xy as -5xy+12xy
so we have
2x^2 - 5xy + 12xy - 30y^2
= x(2x - 5y) + 6y(2x - 5y)
= (2x-5y)(x+6y)
Although this seems to be the popular method taught these days, us old-timers don't use this method.
I have my own quick way where I can do about 5 questions in the time it takes somebody to do one using the above method.
(I wouldn't be at all surprised if other math tutors on here like bobpurley and drwls use the same method I do)
To start solving the equation 3y^2 + 17y + 20 = 0, you can follow these steps:
Step 1: Understand the equation type
This equation is a quadratic equation, which means it is a second-degree polynomial equation. Quadratic equations are typically in the form of ax^2 + bx + c = 0, where a, b, and c are constants.
In our case, the equation is 3y^2 + 17y + 20 = 0, so a = 3, b = 17, and c = 20.
Step 2: Choose a method to solve
There are different methods to solve quadratic equations, such as factoring, completing the square, or using the quadratic formula. In this case, factoring might be the easiest method to use.
Step 3: Factor the equation
To factor the equation, we need to find two numbers that multiply to give the product of the coefficient of the squared term and the constant term (ac), and add up to the coefficient of the linear term (b).
In our equation, a = 3, b = 17, and c = 20. We need to find two numbers that multiply to give (3 * 20) = 60 and add up to 17.
After trying different combinations, we find that 12 and 5 satisfy these conditions (12 + 5 = 17, and 12 * 5 = 60).
So, we can rewrite the equation by splitting the middle term:
3y^2 + 12y + 5y + 20 = 0
Step 4: Group and factor further
Now, we can group the terms in pairs and factor them separately:
(3y^2 + 12y) + (5y + 20) = 0
Factoring out the common factors from each pair:
3y(y + 4) + 5(y + 4) = 0
As we can see, we have a common factor of (y + 4) in both terms. We can factor it out:
(y + 4)(3y + 5) = 0
Step 5: Solve for y
To solve the equation, we set each factor equal to zero and solve for y:
y + 4 = 0 ---> y = -4
3y + 5 = 0 ---> 3y = -5 ---> y = -5/3
So, the solutions to the equation 3y^2 + 17y + 20 = 0 are y = -4 and y = -5/3.
Remember to always double-check your answers by substituting them back into the original equation to ensure they satisfy the equation.