How do I factor 4x²+7x+12?

Question

I have been stuck on this for EVER! No matter what I do, I can't come up with 7x. Any help would be great!

Answer 1

*You can use the Quadtratic Equation which is...

x = [- b +/- V`(b^2 - 4ac))] / 2a

First: you have three values (coefficients) for three variables...
a = 4
b = 7
c = 12

Sec: replace the values with the corresponding variables...

x = [- 7 +/- V`(7^2 - 4(4)(12))] / 2(4)

x = [- 7 +/- V`(7^2 - 4(4)(12))] / 8

x = [- 7 +/- V`(7*7 - 4(4)(12))] / 8

x = [- 7 +/- V`(49 - 4(4)(12))] / 8

x = [- 7 +/- V`(49 - 4(48))] / 8

x = [- 7 +/- V`(49 - 192)] / 8

x = [- 7 +/- V`(- 143)] / 8

*Rule - you can't find the square root of a negative number --- the negative sign becomes an imaginary number (i) & write it in front of the radical sign...

x = [- 7 +/- i V`(143)] / 8

Third: you have two solutions --- one is positive, the other is negative...

a. x = [- 7 + i V`(143)] / 8

x = - 7/8 + (i V`143)/8

b. x = [- 7 - i V`(143)] / 8

x = - 7/8 - (i V`143)/8

Answer 2

Use the quadratic formula which is -b+ or - the square root of (b^2-4ac) all over 2a. b would be 7, a would be 4, and c would be 12. When you use the formula you find that there would be a negative under the square root, so the answer would be imaginary. You basically solve the equation under the square root and get negative 143. When you take the square root of a negative, it depends on what math class you're in. Sometimes the teacher will accept the answer DNE (Does Not Exist) or you have to write it i square root of143 for imaginary. So the answer would be (-7+ or -i square root of 143)/8.

Answer 3

You cannot factor that unless you use the completeing the square method. Search on the internet for explenations.
Another way to solve it would be the quadratic equation.

Answer 4

you look the roots

r = -7 +- (49-4**4*12)/14 Here they are negative

Are you sure there is no sign error

Answer 5

it can't be factored. You have to use quadradic fomula