Question

1. $5w^{3}-25w^{2}+45w$

1. $-12xy^{3}-6xy + 6$

1. $3f^{3}g^{2}+15fg^{3}-27f^{2}g^{2}$

1. $15d^{3}b^{3}-60db^{2}$

1. select all the expressions that are equivalent to $16y^{3}-8y^{2}-20y$.

$square$ $2(8y^{3}-4y^{2}-10y)$
$square$ $4(4y^{3}-2y^{2}-5y)$
$square$ $4y(4y^{2}-2y - 5)$
$square$ $y(16y^{2}-8y - 20)$

which expression above is factored completely?

you do
rewrite each expression as a product of polynomials.

1. $2x + 12$

Explanation:

Problem 4: \(5w^3 - 25w^2 + 45w\)

Step 1: Identify the GCF

The greatest common factor (GCF) of \(5w^3\), \(-25w^2\), and \(45w\) is \(5w\).

Step 2: Factor out the GCF

Divide each term by \(5w\):
\(5w^3 \div 5w = w^2\), \(-25w^2 \div 5w = -5w\), \(45w \div 5w = 9\).
So, \(5w^3 - 25w^2 + 45w = 5w(w^2 - 5w + 9)\).

Step 1: Identify the GCF

The GCF of \(-12xy^3\), \(-6xy\), and \(6\) is \(6\) (we can factor out \(-6\) for simplicity, but \(6\) works too; let's use \(-6\) to make the first term positive).

Step 2: Factor out the GCF

Divide each term by \(-6\):
\(-12xy^3 \div -6 = 2xy^3\), \(-6xy \div -6 = xy\), \(6 \div -6 = -1\).
So, \(-12xy^3 - 6xy + 6 = -6(2xy^3 + xy - 1)\) (or with GCF \(6\): \(6(-2xy^3 - xy + 1)\)).

Step 1: Identify the GCF

The GCF of \(3f^3g^2\), \(15fg^3\), and \(-27f^2g^2\) is \(3fg^2\).

Step 2: Factor out the GCF

Divide each term by \(3fg^2\):
\(3f^3g^2 \div 3fg^2 = f^2\), \(15fg^3 \div 3fg^2 = 5g\), \(-27f^2g^2 \div 3fg^2 = -9f\).
So, \(3f^3g^2 + 15fg^3 - 27f^2g^2 = 3fg^2(f^2 + 5g - 9f)\).

Answer:

\(5w(w^2 - 5w + 9)\)

Problem 5: \(-12xy^3 - 6xy + 6\)