Can somebody please explain to me how to factor trinomials that contain two unknown variables and are complex sum & product??
Examples:
2x^2 + 13xy + 15y^2
11x^2 + 14xy + 3y^2
I understand how to factor trinomials that only have x as the variable, but please someone help with the steps!
There really is not much different ..from what you have been doing with one unknown.
11x^2 + 14xy + 3y^2
(11x + 3y)(x+y)
Does that work?
I will be happy to critique your work on the other.
Yea, that's right.
I just need to know how you arrived to that answer. My teacher wants us to show all the steps involved, etc.
Like this:
3x^2 + 7x + 2=
3x^2 + 6x + 1x + 2=
3x(x + 2) + 1(x + 2)=
(x + 2)(3x + 1)=
You fill in in. I just factored.
ok.. my teacher didn't teach us that method. instead he taught us to factor completely.. so i'm stuck because that's how he wants us to arrive at our answer.
I see. In that case, let me explain the steps to factor trinomials with two unknown variables and complex sum and product.
To factor trinomials with two unknown variables, like the examples you gave, we need to consider the coefficients of the variables. Here are the steps:
Step 1: Multiply the coefficient of the x^2 term and the constant term. For example, in the first trinomial, 2x^2 + 13xy + 15y^2, the product of the coefficient of x^2 (2) and the constant term (15y^2) is 30y^2.
Step 2: Now we need to find two numbers that multiply to give us the product from Step 1 (30y^2), and also add up to give us the coefficient of the xy term (13xy). In this case, the numbers are 10y and 3y because (10y * 3y = 30y^2) and (10y + 3y = 13xy).
Step 3: Rewrite the trinomial by splitting the middle term using the two numbers found in Step 2. The trinomial becomes: 2x^2 + 10xy + 3xy + 15y^2.
Step 4: Now, group the terms into pairs: (2x^2 + 10xy) + (3xy + 15y^2).
Step 5: Factor out the common factors from each pair separately. In the first pair, you can factor out 2x: 2x(x + 5y). In the second pair, you can factor out 3y: 3y(x + 5y).
Step 6: Now, notice that both pairs have a common factor of (x + 5y). Factor that out: (x + 5y)(2x + 3y).
So, the factored form of 2x^2 + 13xy + 15y^2 is (x + 5y)(2x + 3y).
You can follow the same steps to factor the second trinomial, 11x^2 + 14xy + 3y^2. The factored form will be (11x + 3y)(x + y).
I hope this explanation helps you understand how to factor trinomials with two unknown variables using the complex sum and product method.