Factoring four-term polynomials by grouping
Description/Explanation/Highlights
Video Description
This video explains how to factor four-term polynomials by grouping.
Steps and Key Points to Remember
To factor a four-term polynomial, follow these steps:
- Make sure the expression you are factoring has four terms by counting the terms separated by addition or subtraction signs. In the example: \(6x^3+4xy+3x^2y+2y^2\) there are exactly 4 terms: \(6x^3\), \(4xy\), \(3x^2y\), and \(2y^2\).
- To factor this, we will group the polynomial into groups of two terms with common factors using parenthesis. i.e. \((6x^3+4xy)+(3x^2y+2y^2)\)
- Take the common factor or factors out of each group. In this case the first group has 2 and x as common factors and the second group has y as its only common factor. Taking them out leaves us with: \(2x(3x^3+2y)+y(3x^2+2y)\)
- Notice that we now have a common factor of \((3x^2+2y)\) in each term. We can take out that factor giving us the first factor and the remaining part is the second factor! i.e. \((3x^2+2y)(2x+y)\)
- Be aware that if after factoring out common factors from the two groups you are not left with a common factor, you will need to start again by moving some terms around and regrouping to try to find a grouping that will have a common factor. If a grouping can’t be found, then the four-term polynomial does not factor.
- As with any factoring problem, you can apply the rules of polynomial multiplication to multiply the factors together to check. After multiplying, you should have the original four-term polynomial if you factored correctly.
Here are some key points to keep in mind when factoring a four-term polynomial:
- Make two groups of two terms that will have common factors that can be factored out.
- If the first grouping doesn’t leave a common factor in each group after factoring out the common factors, it’s ok to start again and move terms around to try another grouping.
- Be careful when regrouping to make sure the sign is moved with the term.
- If no grouping produces a common factor, the polynomial can’t be factored this way.
Video Highlights
- 00:00 \(6x^3-4xy+3x^2y+2y\) four-term factoring example
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