



 
Hi Rebecca. I'll show you how to do this with a detailed example: Example: Factor x² + 4x  32 = 0. To solve this question, I start by making a box that will reveal the answer. I start by writing the "squared" term in the upper left and the last term (the constant term) in the lower right: I am going to write the factors on the top and the left sides. This is just a table  you multiply the things at the top by the things on the left and put the product inside the corresponding box. First, I know that x² is just x times x: Now comes the hard part. I need to find two numbers that add to +4 (that comes from the +4x middle term) and that multiply to 32. So I start by ignoring the minus sign for a moment and just think about what pairs of numbers multiply to make 32. I'll do it the long way so you can see. Each pair, I try switching the signs (one is positive and the other negative) and add them up. I'm hoping to add to 4. 1 + 32 = 31 (nope) This means the two numbers I'm looking for are 4 and 8. I write them on the diagram. Note that where the column and row meet, I have 32, which is +8 times 4. Now I can fill in the two empty spots. The row "x" times the column "+8" is +8x: And the row "4" times the column "x" is 4x: If you were to add up everything inside the four cells, you should get the original quadratic (once you simplify): x² + (+8x) + (4x) + (32) = x² + 4x  32. The box I worked with reveals the factors of the quadratic: they are the things outside the cells! So the factors of x² + 4x  32 are (x + 8) and (x  4). In other words, x² + 4x  32 = (x + 8) (x  4). Try this method with your question, Rebecca. The trick will be to find a pair of numbers that multiplies to make +10 and that adds to make +7. Hope this helps,
 


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