 # Factoring Polynomials

Directions: What numbers go in the blanks to make the equation true? ### Hint

How would using a visual representation like algebra tiles or an array method make this easier to factor?

The first blank is 6 and the second blank is 2.

Source: Robert Kaplinsky

## Difference of Squares and Sum of Cubes

Directions: Using the digits 0 to 9 at most one time each, place a digit …

1. This is High School? Then if they have a clue about algebra I would expect them to see this as a problem with 2 unknowns, call them A and B, multiply out the factors and solve the resulting equations. In fact by looking at the x cubed term it is “obvious” with this approach that the second number is 2. Anyway, the hint is odd as we have the factors already.

• Thanks again for your contributions Howard. Clearly there are many ways to solve these problems.

2. I like this problem, especially if we use the area model for representing the distributive property of polynomial multiplication. We are about to start factoring this week, I may try this one!

I’d love more examples of factoring questions like this! I didn’t see any more here but if you have another place to look, let me know. 🙂

I took a stab at writing one, not sure how good it is though:

Given 12x^2 + Ax + 20 = ( x + )( x + ), and using integers -9 to 9 at most once each, create a product where A is

a) ODD
b) EVEN
c) as SMALL as possible
d) as LARGE as possible

I confess I haven’t tried it out myself but I thought it would be fun to try!

• OK I think I’d have to change the last number from 20 to maybe 21, for an ODD middle term to be possible. 🙂