In Factoring Polynomials how do I factor 2x^2-15x+7?

Question

Factor:
2x^2-15x+7

Okay, so first what I did was find the sum and product. Which was.
S= -15
P= 14

Then the terms that I can use I got -1 & -14.
So then I rewrited the problem as 2x^2-1x-14x+7
then I did this: 2x(x-1) -7 (2x-1)

Then my answer was: (x-1)(2x-7)

Did I do this right? I don't know for sure. If you could please do this step by step for me so I can understand it better would be helpful. Becauase the second part I didn't get. Which was the 2x(x-1) -7 (2x-1) otherwise I get the problem and what we have to do.

Answer 1

You are using a method I have never seen before, but unfortunately, I don't see the correct answer. Here's my thought process...

If this is supposed to give integer answers, then I could have either a 2 or a 1 as my lead coefficient. I could have either a +/- 1 or 7 for the end value. That still leaves a little guess and check work, but wouldn't 2* -7 get us close to -15?

(2x - 1) (x -7) = 2x^2 - 14x - 1x + 7 = 2x^2-15x+7

Answer 2

where did you s & p ?

start from scratch

2x^2 - 15x + 7
factors of 2 (1*2)
factors of 7 (1*7)

since the middle portion is a negative and the third is a positive
both signs will be negative

now taking 1 & 2 and 1 & 7
match them up so that the products = 15

your answer was 1*2 and 7*1 gives us a negative 9 - wrong

(x-7)(2x-1) is the correct answer

Answer 3

2X^2-15X+7
(2X-1)(X-7)
check:
2X times X = 2X^2
2x times -7 = -14X
-1 times X = -1X
-1 times -7 = 7
gather terms
2X^2-15X+7

Answer 4

You did it incorrectly. You messed up regrouping.
2x^2-1x-14x+7
=2x(x-7)-1(x-7)
=(2x-1)(x-7)

When factoring by grouping, make sure what you have in parentheses is the same.

Answer 5

then I did this: 2x(x-1) -7 (2x-1)
Above is where you went wrong. It should be:
x(2x-1) -7(2x-1)
Then you get (x-7)(2x-1) which is the correct answer.

It was a simple error in factoring.

Answer 6

(x-7)(2x-1)

Answer 7

use the quadratic formula