Question

How to factor 2x^2+5x-3???

Answer 1

Have you learned the quadratic formula?

Answer 2

Yes.
Would this be applied here?

Answer 3

@jim_thompson5910

Answer 4

yes the best way to factor in my opinion is to first find the roots using the quadratic formula. What roots do you get?

Answer 5

25-(24)=1

Answer 6

ok that looks like the value of b^2 - 4ac

Answer 7

notice that since the discriminant is equal to 1, which is a positive perfect square, this means we can factor

Answer 8

I see... so how do we proceed?

Answer 9

I attempted to utilize the AC method when going about factoring the trinomial but ended up with an incorrect result.

Answer 10

so do you have this written down?

\[\Large x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\]
\[\Large x = \frac{-5\pm\sqrt{5^2-4*2*(-3)}}{2*2}\]
\[\Large x = \frac{-5\pm\sqrt{49}}{4}\]

notice how 49 is under the root and NOT 1

Answer 11

Yes; would we proceed by simplifying the division and the square root? -5+/-7/4= 1/2 or -3.

Answer 12

correct, the two roots are 1/2 and -3

Answer 13

if x = 1/2, then we can multiply both sides by 2 to get 2x = 1

then subtract the 1 from both sides to get 2x - 1 = 0

agreed?

Answer 14

Certainly.

Answer 15

then if x = -3, we can add 3 to both sides to get x+3 = 0

Answer 16

I see where you're going now, by discovering the roots, it's much easier to find the factors.

Answer 17

so the two roots

x = 1/2 or x = -3

turns into these two equations

2x-1 = 0 or x+3 = 0

Answer 18

yes, we then use the zero product property to go from `2x-1 = 0 or x+3 = 0` to `(2x-1)(x+3)=0`

Answer 19

the last thing to do is to expand out `(2x-1)(x+3)` and see if you get `2x^2+5x-3`

Answer 20

While this certainly is an easier method, I don't know if in application I will be able to know to multiply the root, x=1/2, by 2 on both sides. What tells us we need to do this?

Answer 21

the goal is to get each root to turn into an equation where the right side is 0

so we can use the fact that `A = 0 or B = 0` turns into `A*B = 0`

Answer 22

you dont' have to multiply by 2, but I don't like fractions which is why I try to get rid of them as soon as possible

Answer 23

you could easily have

x - (1/2) = 0 and x+3 = 0

turn into

(x - (1/2))*(x+3) = 0

but that's a bit more complicated than it needs to be

Answer 24

I guess I would remember to do it as the factors typically need to be written with whole numbers.

Answer 25

yeah that's a good general rule to have so it's as simple as possible

Answer 26

Thank you so much for your thorough response!

Answer 27

you're welcome