Question

how do i factor this

3x^2+11x−20=0

Answer 1

I'll try to explain the method I use (it requires some trial and error but the more you practice, the easier it gets)

I draw a big X on my paper. On the left "prongs" of the X, I pick two factors of the x^2 coefficient (positive 3). On the right "prongs" of the X, I pick two factors of the constant (-15)

Answer 2

Now, when I multiply across the lines, I get 3*5 and 1(-4), or 15 and -4. When I add these together, I get 11 (the coefficient of the x term.) That's the goal.

now, reading the numbers **horizontally** I get 3 and -4 as well as 1 and 5. translating these to binomials, I get (3x-4)(x+5) which is the factorization.

Answer 3

It takes a bit of practice to know what factors to pick, but once you practice enough it'll become second nature.

Answer 4

isnt it 3x+4 and x-5

Answer 5

(3x+4)(x-5) = 3x^2 - 15x + 4x - 20 which gives you -11x instead of +11x

Answer 6

oh

Answer 7

remember you can always check your factoring by multiplying the factors and seeing if it gets back to the original polynomial

Answer 8

yes, but i never get them right

Answer 9

Well, if you use this cross method, you can always check at the first step to make sure it adds up to the middle term. if it doesn't, you can simply pick different factors.

There's another method called the box method, which doesn't require as much guess-and-checking, it's just a bit more involved. https://www.basic-mathematics.com/factoring-using-the-box-method.html