Required Skills
- Factoring using common factors
Factoring Using Common Factors
What are factors? ⇒ When two particular factors of a number are multiplied, the product should be the number itself.
- Example ⇒ Two factors of 20 are 4 and 5.
What are common factors? ⇒ Common factors exist between two numbers when they have the same factors.
- Example ⇒ A common factor between 9 and 12 is 3.
To factor a polynomial using common factors, we:
- Identify a common factor from each term of the expression, if there are any.
- Divide every term by the common factor. This will give you a new polynomial.
- Rewrite the polynomial with the common factor at the beginning, and the new polynomial (in parentheses) next, symbolizing that they're being multiplied.
- Repeat until there are no more common factors.
Solution - Common Factoring
[tex]24x^3y^2+16xy^3+12y^3[/tex]
24, 16 and 12 can all be divided by 4. Therefore, 4 is a common factor:
[tex]= 4(6x^3y^2+4xy^3+3y^3)[/tex]
All of the terms have the variable y. The second two terms have y raised to the power of 3, but because the first term only has y raised to the power of 2, we must factor out y²:
[tex]= 4y^2(6x^3+4xy+3y)[/tex]
We cannot factor this polynomial any further. Therefore, [tex]4y^2(6x^3+4xy+3y)[/tex] is our final answer.
Answer
C. [tex]4y^2(6x^3+4xy+3y)[/tex]
