SOLUTION: whats the polynomials factor of x^2-7x+6 ?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: whats the polynomials factor of x^2-7x+6 ?      Log On


   

Question 76507: whats the polynomials factor of x^2-7x+6 ?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)
In order to factor 1%2Ax%5E2%2B-7%2Ax%2B6, first we need to ask ourselves: What two numbers multiply to 6 and add to -7? Lets find out by listing all of the possible factors of 6


Factors:

1,2,3,6,

-1,-2,-3,-6,List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to 6.

1*6=6

2*3=6

(-1)*(-6)=6

(-2)*(-3)=6

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to -7? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -7

||||
First Number|Second Number|Sum
1|6|1+6=7
2|3|2+3=5
-1|-6|-1+(-6)=-7
-2|-3|-2+(-3)=-5
We can see from the table that -1 and -6 add to -7.So the two numbers that multiply to 6 and add to -7 are: -1 and -6 Now we substitute these numbers into a and b of the general equation of a product of linear factors which is: %28x%2Ba%29%28x%2Bb%29substitute a=-1 and b=-6 So the equation becomes: (x-1)(x-6) Notice that if we foil (x-1)(x-6) we get the quadratic 1%2Ax%5E2%2B-7%2Ax%2B6 again


So in other words, x%5E2-7x%2B6 factors to %28x-1%29%28x-6%29