   SEARCH HOME Math Central Quandaries & Queries  Question from KIM, a teacher: please factor and solve s1^2 - 10s1 - 200 = 0 We have two responses for you

Kim,

When factoring a quadratic expression (when the number in front of the squared variable is 1, or implied that way), you want to find two numbers that add together to give the middle value and multiply together to give the scalar value on the right.

For example, r2 + 6r - 27.

I need two numbers that add to +2 and multiply to -27. Those are +9 and -3. So I factor it as:

(r + 9) (r - 3)

You can do exactly the same thing with your question. What two numbers add to -10 and multiply to -200?

Cheers,
Stephen La Rocque.

Kim,

There is another method you can use if you don't see the factors. The method is to complete the square. Again this works nicely if the coefficient of the square term is 1. Let's look at Stephen's example

r2 + 6r - 27

To complete the square using the terms r2 + 6r I add the square of half the coefficient of the linear term, so here I add (6/2)2 = 32 = 9 since r2 + 6r + 9 = (r + 3)2. Because I am going to add 9 to the expression I need to subtract 9 also to maintain the equality.

r2 + 6r - 27
= r2 + 6r + 9 - 27 - 9
=(r+3)2 - 36
= (r + 3)2 - 62

If you recognize this as a difference of squares you can continue

(r + 3)2 - 62
=(r + 3 - 6)(r + 3 + 6)
= (r - 3)(r + 9)

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.