Question

HELP FAST PLEASE!!
Factor the following polynomial

Answer 1

Required Skills

1. 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:

1. Identify a common factor from each term of the expression, if there are any.
2. Divide every term by the common factor. This will give you a new polynomial.
3. Rewrite the polynomial with the common factor at the beginning, and the new polynomial (in parentheses) next, symbolizing that they're being multiplied.
4. Repeat until there are no more common factors.

Solution - Common Factoring

`24x^3y^2+16xy^3+12y^3`

24, 16 and 12 can all be divided by 4. Therefore, 4 is a common factor:

`= 4(6x^3y^2+4xy^3+3y^3)`

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:

`= 4y^2(6x^3+4xy+3y)`

We cannot factor this polynomial any further. Therefore,
`4y^2(6x^3+4xy+3y)` is our final answer.

Answer

C.
`4y^2(6x^3+4xy+3y)`