Ok can someone please help me understand how to do this problem.......?

Question

I'm not just looking for the answer but i need all the steps it takes to get the answer so that way i can understand how to do the rest of my problems for my homework. Thanks

Factor each trinomial. Factor out all common monomials first (including -1 if the lead coefficient is negative). If a trinomial is prime, so indicate.

Here is the problem:

8x^2 - 10x + 3

Answer 1

Ok..to factor the trinomial, you have to express the given trinomial as the product of two (because the highest degree, x^2, is two) monomials of degree 1 (x^1).

To find the factors of 8x^2 - 10x +3, multiply the first and last term, i.e 8x^2 and 3. Their product is 24x^2.

Next, spilt the middle term ( -10x) into two terms so that the product of the two terms is 24 x^2.
Here, we can split -10x into -6x-4x (they add upto -10x).

We can now rewrite the trinomial as:
8x^2 -6x - 4x +3
In the first two terms (i.e 8x^2 and -6x) we can see that 2x is a common factor (both terms are divisible by 2 and x)

Rewritten trinomial:
2x(4x - 3) - 4x+3.

(or)
2x(4x-3)-1(4x-3). Here, 4x-3 repeats..so, it's a factor.
your answer:
=> (2x-1)(4x-3).
Those are your factors.
So, basically
1. Arrange all the terms in descending order of their power (x^2, then x, then the constant)
2.Split the middle term (the x term) so that the product of the two parts gives you the product of the first and last term (i.e x^2 and constant).
3.Take out the common factors.
4. Write the expression as the product of the factors.
Hope this stuff is clear..
cheers

Answer 2

Use a big "X" method by writing a big "X" on a piece of paper.

First Step: multiply the first coefficient (8) with the last coefficient (3) = 24 and write 24 on the top of the "X"

Second Step: write the middle coefficient (-10) on the bottom of the "X"

Third step: find two numbers that give you 24 when multiplied together and -10 when added or subtracted from each other

two numbers: (-4)(-6) = 24
- 4 - 6 = -10

fourth step: factored form: (x - 4)(x - 6)

Answer 3

8*3=24
24 has to be factorized in such a way tha addition/subtraction of resultion no gives -10
24 has factors:
2,2,2,3
-6 and -4 are the required ones.
-6-4=-10
8x^2-6x-4x+3=0
2x(4x-3)-1(4x-3)=0
(4x-3)(2x-1)=0
x=3/4 and x=1/2