I think trial and error might be the best way to figure out what’s going on with factoring. Trial and error with a little bit of nudging goes pretty far here.

I think you meant x^2-13x+22? Or maybe you didn’t. More examples like x^2-8x-20 might be helpful to get confident with negative products. Regardless, this is a good way to work toward an understanding of sums and products. I eventually like working in (x+a)(x+b) as the last expansion you’ll ever need ðŸ˜‰

If students are armed with the addition and multiplication tables, factoring x^2 + sx + p can be solved by finding a location in the tables where the sum s appears in the addition table while the product p appears in the same location in the multiplication table…

I think you meant x^2-13x+22? Or maybe you didn’t. More examples like x^2-8x-20 might be helpful to get confident with negative products. Regardless, this is a good way to work toward an understanding of sums and products. I eventually like working in (x+a)(x+b) as the last expansion you’ll ever need ðŸ˜‰

If students are armed with the addition and multiplication tables, factoring x^2 + sx + p can be solved by finding a location in the tables where the sum s appears in the addition table while the product p appears in the same location in the multiplication table…