There are common questions that students have in algebra. We answer a couple here on the following topics:
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My teacher taught us a method she called “guess and check” or “trial and error”. It is so confusing and I have trouble if the coefficients are big especially if the coefficient of the first term is other than 1. Do you know an easy way?
Yes, I do.We will use factoring by grouping sometimes called the“box method”.You will look at the factors of ac that add to b.Then factor by grouping or arrange the terms in a box and factor.It works ever time.
Let us look at an example:Factor 2x2 – 15x + 18.Notice a = 2, b = -15, and c = 18.
Step 1: Calculate ac = 36 where b = -15
Step 2:Find the factors of ac = 36.They are:
1 and 36
- 1 and - 36
2 and 18
- 2 and - 18
3 and 12
- 3 and - 12
4 and 9
- 4 and - 9
Step 3: The only pair that adds to – 15 is - 3 and – 12.Write the polynomial as 2x2 – 3x – 12x+ 18 .
Step 4: Factor by grouping: Put the first two terms in parentheses and the last two terms separated by a plus sign. ( 2x2 – 3x) + ( – 12x+ 18).
Factor a common factor out of the first grouping and a common factor from the last grouping:
x ( 2x – 3) + ( - 6) ( 2x - 3).(Notice we factored (- 6) from the last two terms.)
Then your answer is (x – 6 )( 2x – 3)
Example on your own:
Do you want to try one?Factor 3x2 + 10x – 8 following the steps above.
Solution:The product of ac = -24 and the factors you should have selected were - 2 and 12.
The polynomial you will then factor by grouping is 3x2 – 2x + 12x – 8 .
Your solution after factoring by grouping is (3x – 2)(x + 4)
Zach asks, "In using the distributive property to simplify algebraic expressions do I distribute or add first. For example, do I subtract 8 - 9 first in 8 - 9 (7 - 5 x )?"
Zach, always remember PEMDAS (Please Excuse My Dear Aunt Sally) for the "order of operations" with algebraic operations. We do multiplication and division before addition and subtraction. Therefore, use the distributive property with multiplication BEFORE subtracting 8 - 9. To make things easier for you, consider multiplying by - 9. Your simplification will look like this:
8 - 9 (7 - 5 x )
= 8 - 9 (7) + (- 9 ) ( - 5)
= 8 - 63 + 45
Now add (subtract) left to right and you have:
= - 55 + 45
= - 10
Mason asks, "Are there good algebra videos?"
Algebra: Videos from beginning Algebra through Algebra II (Data Math).
Algebra I Worked Examples: Sample problems worked from Algebra I.
Developmental Math 2: Oodles of worked examples from Algebra through Algebra II
ck12.org Algebra I Examples: Great review topics to make sure you understand Algebra I topics.
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