Final answer:
The greatest common factor (GCF) of the polynomial 4xy² + 40x²y² - 56y³ is 4y³. The factored form of the polynomial is 4y³(10x²+x-14y)/y. Option B is correct.
Step-by-step explanation:
A polynomial can be written as the product of its factors having a degree less than or equal to the original polynomial. The process of factoring is called factorization of polynomials.
Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable.
The greatest common factor (GCF) of the polynomial 4xy² + 40x²y² - 56y³ is 4y³. To factor out the GCF, you divide each term by the GCF and write the result in parentheses.
Dividing each term by 4y³ gives:
- 4xy² ÷ 4y³ = x/y
- 40x²y² ÷ 4y³ = 10x²/y
- -56y³ ÷ 4y³ = -14
Therefore, the factored form of the polynomial is 4y³(x/y + 10x²/y - 14), which can be simplified to 4y³(10x²+x-14y)/y.