How do you factor the expression 4s^2-22s+10?

1 Answer
Jan 19, 2017

4(x-5)(x-1/2)

Explanation:

We need to find the roots of the equation:

4s^2 - 22s + 10 = 0.

We can first divide the entire expression by 2:

2s^2 - 11s + 5 = 0. Although not necessary, this does simplify the procedure just a little bit.
Using the quadratic formula:

x = (-b +- sqrt(b^2-4ac))/(2a), where

a is the coefficient of x^2
b is the coefficient of x, and
c is the constant term.

So, x = (11 +- sqrt81)/4 => x = 5 or x = 1/2.

The formula for factoring a quadratic is:

a(x - r_1)(x - r_2) where r_1,r_2 the two roots.

We still have to remember that although the roots of

4s^2 - 22s + 10 = 0

are the same as those of

2s^2 - 11s + 5 = 0,

the original value for a is 4, not 2.

So,

4s^2 - 22s + 10 = 4(x-5)(x-1/2)