SOLUTION: Hi Everyone, I am supposed to factor the following polynomials completely: (a) 14x^2-20x+6 & (b) -3s^2-10s+8 Could someone please help me understand what it is I am suppose

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi Everyone, I am supposed to factor the following polynomials completely: (a) 14x^2-20x+6 & (b) -3s^2-10s+8 Could someone please help me understand what it is I am suppose      Log On


   

Question 84093: Hi Everyone,
I am supposed to factor the following polynomials completely:
(a) 14x^2-20x+6 & (b) -3s^2-10s+8
Could someone please help me understand what it is I am supposed to do here? Please, Thank You
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You're supposed to find the roots of the equations. Since the
largest exponent is 2 (x^2), there are 2 roots in each case.
The roots are values for the unknown that make the equation 0.
Say the roots are r1 and r2, then
(x - r1)(x - r2) = 0
If you then make x = r1,
(r1 - r1)(r1 - r2) = 0 this is true
If you make x = r2, then
(r2 - r1)(r2 - r2) = 0 this is true also
How do you find the roots? Use the so-called quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a = 14
b = -20
c = +6
x+=+%28-%28-20%29+%2B-+sqrt%28+%28-20%29%5E2-4%2A14%2A6+%29%29%2F%282%2A14%29+
x+=+%2820+%2B-+sqrt%28400+-+336%29%29%2F28+
x+=+%2820+%2B-+sqrt%2864%29%29%2F28+
x+=+%2820+%2B+8%29+%2F+28
and
x+=+%2820+-+8%29+%2F+28
or, x+=+1 and x+=+3%2F7
So, your factors are
%28x+-+1%29%28x+-+%283%2F7%29%29
Do these multiplied together give you the original equation?
%28x+-+1%29%28x+-+%283%2F7%29%29+=+x%5E2+-%2810%2F7%29x+%2B+3%2F7
Multiplying both sides by 14,
14%2A%28x+-+1%29%28x+-+%283%2F7%29%29+=+14x%5E2+-+20x+%2B+6
So, 1 and 3/7 are the factors.
The other equation is factored in the same manner