Factoring Trinomials 10 Points?

6x^2 -19x + 3

=(6x-1)(x-3) answer//

You simply have to look at the factors of 6 (6&1 or 2&3) and look at the factors of 3 (3&1) and then figure it out mentally.

In this example it has to be (6x - 1)(x - 3)

You need two minus signs because that's the only way you can get -19x and +3

wen a has a constant value u multiply it wid d constant dat is d third term of d whole algebric expression

d above statement didnt make anything clear rite

so hear

in 6x^2-19x+3

u multiply 6 wid 3 n get 18....so now u need to split -19x into two terms such dat after mutliplyin them u get positive 18

so d terms r

-18x n -1x

6x^2-18x-x+3

6x(x-3)-1(x-3) here u took 6x n -1 common frm 6x^2-18x n -x+3 respectively

(6x-1)(x-3) r d two factors....

hope u got it!

look at the factors of both 6 and 3, arrange them in a way that gives u (-19) after addition, the best factors to take for 6 are 1 and 6 , and for 3 are 1 and 3

........ _

.........| |

(6x - 1)(x - 3)

..|_______|

-18x - x = - 19x

You shall find the solutions of the associated equation:

6x^2-19x+3=0

The solutions are:

x=3 and x=1/6

Then:

6x^2-19x+3= (x-3)(x-1/6)

Ok, guess you didn't bother reading last post

We need factors of (6)(3) = 18 which add up to -19.

(-18)(-1) works, so split up middle term like so

6x² -18x - x + 3

=6x(x-3)-1(x-3)

=(6x-1)(x-3)

first multiply the 1st coefficient(a) with the constant(c) and find it factor that when you add, is equal to the 2nd coefficient(b).

ac = 18, its factors that when you add is equal to -19 are (-18 and -1)

then have it in this form,

6x^2 - 18x - x + 3 = 0

6x(x -3) - (x - 3) = 0 --------------->factor out (x-3)

(x-3)(6x - 1) = 0

6x² - 19x + 3 = 0

x² - 19/6x = - 1/2

x² - 19/12x = - 1/2 + (- 19/12)²

x² - 19/12x = - 72/144 + 361/144

(x - 19/12)² = 289/144

x - 19/12 = +/- 17/12

= x - 19/12 - 17/12, = x - 36/12, = x - 3

= x - 19/12 + 17/12, = x - 2/12, = x - 1/6, = 6x - 1

Answer: (x - 3)(6x - 1)

Proof:

= (x - 3)(6x - 1)

= (x[6x]) + (x[- 1]) + (- 3[6x]) + (- 3[- 1])

= 6x² + (- x) + (- 18x) + 3

= 6x² - x - 18x + 3

= 6x² - 19x + 3

Not Factorable.

Thre Are No Terms Which We Can Factor.

∆=19^2-4*6*3=289

x=(19+√289)/12=3

or x=(19-√289)/12=1/6