Remove the largest possible common factor. Check your answer by multiplication $$ 14 x^{4}+21 x^{3}+28 x $$ Factor out the greatest common factor. $$ 14 x^{4}+21 x^{3}+28 x=\square $$

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First, identify the greatest common factor (GCF) of the coefficients and the variable parts:

1. The coefficients $$14$$, $$21$$, and $$28$$ share a common factor of $$7$$.
2. The variable part $$x^4$$, $$x^3$$, and $$x$$ have a common factor of $$x$$.

Thus, the GCF is $$7x$$.

Now, factor $$7x$$ out of each term:

$$
\begin{aligned}
14x^4 &= 7x(2x^3),\[5mm]
21x^3 &= 7x(3x^2),\[5mm]
28x   &= 7x(4).
\end{aligned}
$$

So the expression becomes:

$$
14x^4 + 21x^3 + 28x = 7x\left(2x^3 + 3x^2 + 4\right).
$$

To verify by multiplication, distribute $$7x$$:

$$
7x \cdot 2x^3 = 14x^4,\quad 7x \cdot 3x^2 = 21x^3,\quad 7x \cdot 4 = 28x.
$$

Each term matches the original expression.

Thus, the factorization is:

$$
14x^4 + 21x^3 + 28x = 7x\left(2x^3 + 3x^2 + 4\right).
$$
Factor out $$7x$$ from the expression: $$ 14x^4 + 21x^3 + 28x = 7x(2x^3 + 3x^2 + 4) $$ To check, multiply $$7x$$ by each term inside the parentheses: $$ 7x \times 2x^3 = 14x^4,\quad 7x \times 3x^2 = 21x^3,\quad 7x \times 4 = 28x $$ This matches the original expression, confirming the factorization is correct.

Remove the largest possible common factor. Check your answer by multiplication \[ 14 x^{4}+21 x^{3}+28 x \] Factor out the greatest common factor. \( 14 x^{4}+21 x^{3}+28 x=\square \)

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