We factor in two steps:

1. Separate the greatest common factor from each of the terms. In this case, $\textrm{GCF}(3x,12) = 3,$ so \begin{align*} 3x+12 &= \\[3pt] (3\cdot x)+(3\cdot 4).& \end{align*}
2. Place the common factor in front of the parentheses, leaving whatever remains inside the parentheses: \begin{align*} (3\cdot x)+(3\cdot4) &= \\[3pt] 3(x+4) & \end{align*}

Thus, the factored form of the expression is $3(x+4).$

We factor in two steps:

1. Separate the greatest common factor from each of the terms. In this case, $\textrm{GCF}(8a, 24) = 8,$ so \begin{align*} 8a+24 &=\\[3pt] (8\cdot a) + (8 \cdot 3). \end{align*}
2. Place the common factor in front of the parentheses, leaving whatever remains inside the parentheses: \begin{align*} (8\cdot a) + (8 \cdot 3) &= \\[3pt] 8(a+3) \end{align*}

Thus, the factored form of the expression is $ 8(a+3).$

We factor in two steps:

1. Separate the greatest common factor from each of the terms (ignoring any negative signs). In this case, $\textrm{GCF}(30y,36) = 6,$ so \begin{align*} 30y-36 &= \\[3pt] (6\cdot 5y)-(6\cdot 6). & \end{align*}
2. Place the common factor in front of the parentheses, leaving whatever remains inside the parentheses: \begin{align*} (6\cdot 5y)-(6\cdot 6) &= \\[3pt] 6(5y-6) & \end{align*}

Thus, the factored form of the expression is $6(5y-6).$

Both terms are negative, so we begin by factoring out a negative sign:

\begin{align*} -36a-3 &= \\[3pt] -(36a+3). & \end{align*}

Then, we continue factoring in two steps:

1. Separate the greatest common factor from each of the terms. In this case, $\textrm{GCF}(36a,3) = 3,$ so \begin{align*} -(36a+3) &= \\[3pt] -(3 \cdot 12a + 3 \cdot 1). & \end{align*}
2. Place the common factor in front of the parentheses, leaving whatever remains inside the parentheses: \begin{align*} -(3 \cdot 12a + 3 \cdot 1) &= \\[3pt] -3(12a+1)& \end{align*}

Thus, the factored form of the expression is $-3(12a+1).$

We factor in two steps:

1. Separate the greatest common factor from each of the terms. In this case, $\textrm{GCF}(20a,28b) = 4,$ so: \begin{align*} -20a-28b &=\\[3pt] (-4\cdot 5a)+(-4\cdot 7b) \end{align*}
2. Place the common factor in front of the parentheses, leaving whatever remains inside the parentheses: \begin{align*} (-4\cdot 5a)+(-4\cdot 7b) &=\\[3pt] -4(5a+7b) \end{align*}

Thus, the factored form of the expression is $ -4(5a+7b).$

We factor in two steps:

1. Separate the greatest common factor from each of the terms. In this case, $\textrm{GCF}(42m,54n) = 6,$ so \begin{align*} -42m-54n &=\\[3pt] (-6\cdot 7m)+(-6\cdot 9n) . \end{align*}
2. Place the common factor in front of the parentheses, leaving whatever remains inside the parentheses: \begin{align*} (-6\cdot 7m)+(-6\cdot 9n) &=\\[3pt] -6(7m+9n) \end{align*}

Thus, the factored form of the expression is $ -6(7m+9n).$

We factor in two steps:

1. Separate the greatest common factor from each of the terms (ignoring any negative signs). In this case, $\textrm{GCF}(15p, 9q, 21) = 3,$ so \begin{align*} 15p - 9q +21 &= \\[3pt] (3\cdot 5p)- (3 \cdot 3q)+(3\cdot 7) . & \end{align*}
2. Place the common factor in front of the parentheses, leaving whatever remains inside the parentheses: \begin{align*} (3\cdot 5p)- (3 \cdot 3q)+(3\cdot 7) &= \\[3pt] 3(5p-3q+7)& \end{align*}

Thus, the factored form of the expression is $3(5p-3q+7).$

We factor in two steps:

1. Separate the greatest common factor from each of the terms (ignoring any negative signs). In this case, $\textrm{GCF}(24x, 40y, 72) = 8,$ so \begin{align*} 24x + 40y - 72 &= \\[3pt] (8\cdot 3x)+(8 \cdot 5 y) - (8\cdot 9) . & \end{align*}
2. Place the common factor in front of the parentheses, leaving whatever remains inside the parentheses: \begin{align*} (8\cdot 3x)+(8 \cdot 5 y) - (8\cdot 9) &= \\[3pt] 8(3x+5y-9)& \end{align*}

Thus, the factored form of the expression is $ 8(3x+5y-9).$

We factor in two steps:

1. Separate the greatest common factor from each of the terms (ignoring any negative signs). In this case, $\textrm{GCF}(18x, 6y, 12) = 6,$ so \begin{align*} 18x + 6y - 12 &= \\[3pt] 6\cdot 3x+6 \cdot y-6\cdot 2 . & \end{align*}
2. Place the common factor in front of the parentheses, leaving whatever remains inside the parentheses: \begin{align*} 6\cdot 3x+6 \cdot y-6\cdot 2 &= \\[3pt] 6(3x+y-2)& \end{align*}

Thus, the factored form of the expression is $6(3x+y-2).$