Factor out the greatest common factor from each polynomial. xy−5xy2

Question

Factor out the greatest common factor from each polynomial.  xy−5xy2

jgardner33v4 · Accepted Answer

Step 1
The greatest common factor is a factor which is present in all the terms of an expression with some constant multiple .We can simplify the algebraic expressions by identifying their greatest common factors.
We can factor out the greatest common factor from an expression by writing the multiple of this factor for the terms and by writing this common factor outside the parenthesis. To identify the greatest common factor of the constant numbers, we can use prime factorization technique.
Step 2
Consider the expression

x y - 5 x y^{2}

.
We have to factor out the greatest common factor out from the expression.
To identify the factors, we can write the terms as,

x y = x \times y

5 x y^{2} = 5 \times x \times y \times y

Thus, we have one x and one y as common for both the terms. Therefore, we need to factor out xy as the greatest common factor of the expression .
Thus, we get,

x y - 5 x y^{2} = x y (1 - 5 y (1))

=xy(1-5y)
Hence, we have

x y - 5 x y^{2} = x y (1 - 5 y)

.

Factor out the greatest common factor from each polynomial. xy-5xy^{2}

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