algebra......?

Question

can you please explain how to factor problems like this:

10x^2 - 7x - 6 = 0

i don't understand the ones with a number in front of the x squared.

thanks everyone!

Answer 1

i explained it here... :)

http://artpad.art.com/?jnm9o81dc478

Answer 2

Ok, look at the factors of the coefficient of the x^2. They are 1, 2, 5, 10. Now look at these factors and see which ones would add up to the coefficient of the x (-7) and also multiply to 10. It can be any combination of positive or negative numbers to reach the negative 7 and multiply to 10. As you can see, 5 and 2 add up to 7 and 5 *2 = 10, so you want to use -5 and -2 to add up to -7. So now your factoring looks something like this:
(-2x + ?) (-5x + ?)
Now to find the ?. Ask yourself, what are the factors of 6? 1, 2 ,3,6. Which of these, when multiplied together, will give me a negative 6 (either can be positive or negative). Therefore it has to be -1 * 6 or 6 * -1.
Now put -1 and 6 in for the question marks, and see if it FOILs out to be the same equation, otherwise switch them and try again. I'm going to put the negative 1 with the -2x and the with the -5x, giving you (-2x -1) (-5x + 6). Foiling it out, you get 10x - 12x + 5x -6 = 10x - 7x - 6. Alternately, you could use the Quadratic formula (it will always work, but takes longer) and convert it to the factors-- the quadratic formula would give you 6/5 and -1/2 as answers; The signs are opposite of the factoring and the numerator is the first coefficient and the denominator is the the number added or subtracted. So, 6/5 would turn into -5x + 6 (the sign changes).

Answer 3

It's a little more complicated. You need to factorise both the 10 and the -6 to produce combinations whose products add to -7. (Or you can think of it as factorising 10 and 6 to produce combinations whose products subtract to give -7.)

So, for instance, 10 can be factored as 1 and 10, or 2 and 5; 6 can be factored as 1 and 6, or 2 and 3. If we use the factors 1 and 10, and 2 and 3, we can combine them as follows:
1×2 and 10×3: 2 and 30, subtract to get ±28.
or 1×3 and 10×2: 3 and 20, subtract to get ±17.

In this case the combination that works is 10=2×5, 6=6×1; we can make the products 2×6 = 12 and 5×1 = 5, which subtract to ±7 which is what we want.

That means the 2 and 1 must be in one bracket and the 5 and 6 in the other; also, we want a -12 and a +5 to make -7, so the negative sign must be on the 6. So the factorisation is
(2x + 1) (5x - 6)
and therefore the solutions are x = -1/2, x = 6/5.

Answer 4

When there is a number in present of the variable x^2,you should first of all,multiply it by the constant c and get the product
so multiplying 10 by -6,we get -60.Now find two numbers,whose product is -60 and whose sum is -7(the coefficient of x).These are -12 and +5.Now break up ,the middle term of the expression into -12x and 7x and factor the trinomial by grouping
10x^2-7x-6
=10x^2-12x+5x-6
=2x(5x-6)+1(5x-6)
=(5x-6)(2x+1)

Answer 5

the easiest way to factor poylnomials is to first find out the factors of the first number (in this case 10x^2)
factors of 10: 1,2,5,10. (each will have an x to get x^2)

next figure out the factors of the last number in the polynomial (in this case 6)
factors of 6: 1,2,3,6. (note that this is a -6 so one of the two factors is going to be negative)

the rest is trial and error. substitute each factor of ten in the first spot of both binomials and the factors of 6 in the second spot. eventually you come up with (2x+1)(5x-6).

finally multiply out the two binomials to check if you are right (remember FOIL?)

in this case 2x * 5x = 10x^2
(2x * -6 = -12x)...(1 * 5x = 5x)...-12x + 5x = -7x
1 * -6 = -6

put it all together.........10x^2 - 7x - 6.

hope it helps.

Answer 6

you do it the same way, it's just a little more tricky because there are more combinations of factors you can put together.

10x^2 - 7x - 6 = 0

this one is different. it doesn't matter how many combinations of factors you try, it needs to be done by putting the values into the quadratic equation.

Answer 7

10x^2 -- 7x -- 6 = 0
=> 10x^2 -- 12x + 5x -- 6 = 0
=> 2x(5x -- 6) + 1(5x -- 6) = 0
=> (5x -- 6)(2x + 1) = 0
rest you can, for x = 6/5, --1/2

Answer 8

ok. 10x^2 means there are ten x^2's
to factor, u have to start by taking out the GCF
there is none here
sry cant remembr more

Answer 9

(5x - 6) (2x + 1)

trial and error

Answer 10

(2x + 1)(5x - 6)