Factoring Help?

Question

Factor the following using trial factors.

2x^3 - 11x^2 + 5x

I think I'm supposed to find a common factor for x, but im not sure.
Thanks in advance.

Answer 1

Factor: 2x^3 - 11x^2 + 5x

First: find the greatest common factor which is, "x"...

x(2x^2 - 11x + 5)

Sec: factor the expression in parenthesis > multiply the 1st & 3rd coefficient to get "10." Find two numbers that give you "10" when multiplied & "-11" (2nd/middle coefficient) when added/subtracted. The numbers are: (-10 & -1).

Third: rewrite the expression with the new middle coefficients...

2x^2 - 10x - x + 5

*With 4 terms --- group "like" terms....

(2x^2 - x) - (10x + 5)
x(2x - 1) - 5(2x - 1)
(2x-1)(x-5)

Now, combine the sets of parenthesis with the greatest common factor which is, "x"...

x(2x-1)(x-5)

Answer 2

2x^3-11x^2+5x

Well, we know that each of the three terms have an x in them. This means that we can factor it out.

x(2x^2-11x+5)

Note that if we multiply this out again, it will be the same as the beginning.

Now, we have to see what can let us factor the inside of the parentheses. We know that the numbers we pick must add up to -11 and produce a product of 5. We also know that we will be using 2 in the first term.

So,

x(2x+a)(x+b)

We don't know what a and b are yet. (2x)(b) +(ax) must equal -11 and ab must equal 5. So, what are some factors of 5? Well, 5 and 1, and -5 and -1. So, let's try them.

x(2x+5)(x+1) <--Doesn't work because when we multiplly it out using FOIL, it is not the same as the original equation.

x(2x+1)(x+5) <--Doesn't work

x(2x-5)(x-1)
x(2x-1)(x-5) Works!

I hope that this helps.

Answer 3

First, factor out the only number they have in common, x. That'll simplify things. Then you'll have:

x ( 2x^2 -11x + 5).

Then just factor the factor in parentheses like a quadratic:

x ( 2x - 1)( x - 5 ).

Voila! Hope this helps, if you're having trouble factoring the quadratic equation, send another question. Good luck.

Answer 4

2x^3 - 11x^2 + 5x

Your first step would be to factor out x.

x(2x^2 + 11x + 5)

Now, write it in this form, and plug and test.

x(2x + ?)(x + ?)

What you want to test, in the question marks, are factors of 5. Since 5 is prime, test 1 and 5; you want to test if the sum of the outer terms and inner terms will be 11.

For (2x + 1)(x + 5), our outer product is 10x and our inner is x; added together, it gives 11x, so we are correct in the factorization, and our answer is

x(2x + 1)(x + 5)

Had we tried 5 and 1, then we would have had
(2x + 5)(x + 1); the outer product would be 2x, and the inner product would be 5x, for a total of 7x, which does NOT equal the middle term, 11x.

Answer 5

Okay, so first, the only common factor between all of them is X, so tak out the x, and you get x(2x^2-11x-5) Then, you just factor out the problem, because now you can solve it. so you go
x(2x-?)(x-?) so it is x(2x-1)(x-5) there is your answer hope this helps!!! Good luck in algebra!!!

Answer 6

2x^3 - 11x^2 + 5x
= x(2x^2 - 11x + 5) ---yes you do common factor!
= x(2x - 1)(x - 5) ----just factor it



and if it is all equal to 0, then x must be equal to 0, 1/2, or 5
ignore if its not equal to 0!!!!

Answer 7

x(2x^2-11x+5)
x(2x-1)(x-5)

Answer 8

do the foil thing maybe? i came up with (2x-1)(x-5)(x)

Answer 9

2x^3-11x^2+5x
=x(2x^2-11x+5)
=x(2x^2-x-10x+5)
=x{x(2x-1)-5(2x-1)}
=x(2x-1)(x-5)

Answer 10

www.algebrahelp.com