IM Alg1.7.7 Lesson: Rewriting Quadratic Expressions in Factored Form (Part 2)
The product of the integers 2 and -6 is -12.
List all the other pairs of integers whose product is -12.
Of the pairs of factors you found, list all pairs that have a positive sum. Explain why they all have a positive sum.
Of the pairs of factors you found, list all pairs that have a negative sum. Explain why they all have a negative sum.
These expressions are like the ones we have seen before. Each row has a pair of equivalent expressions. Complete the table. If you get stuck, consider drawing a diagram in the applet below.
These expressions are in some ways unlike the ones we have seen before. Each row has a pair of equivalent expressions. Complete the table. If you get stuck, consider drawing a diagram in the applet above.
Name some ways that the expressions in the second table are different from those in the first table (aside from the fact that the expressions use different numbers).
Consider the expression .
Complete the first table with all pairs of factors of 100 that would give positive values of , and the second table with factors that would give negative values of .
For each pair, state the value they produce. (Use as many rows as needed.)
Consider the expression . Complete the first table with all pairs of factors of -100 that would result in positive values of , the second table with factors that would result in negative values of , and the third table with factors that would result in a zero value of .
For each pair of factors, state the value they produce. (Use as many rows as there are pairs of factors. You may not need all the rows.)
Write each expression in factored form:
How many different integers can you find so that the expression can be written in factored form?