Students will be ale to factor quadratics that contain negative numbers.
Students will be able to factor quadratic equations when the "a" value is not equal to 1 (A/B level)
Multiply out (either with an area model or distribution) the four pairs of binomials below. You should do them on your own paper; you'll want to be able to look back at them to answer the questions below.
Remember that quadratics often have the form:
In these examples, the "a" value is 1.
Question 1
1.
When both numbers (the 9 and 5 in the example above) are positive, what is true about the "b" and "c" values?
Question 2
2.
When the "bigger" number (9 in this case) is negative and the smaller number (5) is positive, what is true about the "b" and "c" values?
Question 3
3.
When the "bigger" number (9 in this case) is positive and the smaller number (5) is negative, what is true about the "b" and "c" values?
Question 4
4.
When both numbers are negative, what is true about the "b" and "c" values?
Finding factors that add to a specific number is part of this process. Some people can do this pretty easily, but others need a more clear process, especially when negative numbers are involved. Try the problems below.
Question 5
5.
What two numbers multiply to equal 20 and add to equal 12?
Question 6
6.
What two numbers multiply to equal -30 and add to equal -1
Question 7
7.
What two numbers multiply to equal 30 and add to equal -13
If that part was difficult, the video below describes an organizational tool and process to help figure out those numbers.
Use the skill you just learned and the patterns you recognized from A5-2 to factor the quadratics below. Some people find they need to do the work on paper and some don't. When there are negatives, I often find that scratch paper is helpful.
Question 8
8.
Factor the equation below.
Question 9
9.
Factor the equation below.
Question 10
10.
Factor the equation below.
If you struggled with that, watch the video below.