Đáp án:

$\begin{array}{l}
21)\\
{x^2} + 6x + 5\\
 = {x^2} + 6x + 9 - 4\\
 = {\left( {x + 3} \right)^2} - {2^2}\\
 = \left( {x + 3 + 2} \right)\left( {x + 3 - 2} \right)\\
 = \left( {x + 5} \right)\left( {x + 1} \right)\\
22){x^2} + 4x - 21\\
 = {x^2} + 4x + 4 - 25\\
 = {\left( {x + 2} \right)^2} - {5^2}\\
 = \left( {x + 2 - 5} \right)\left( {x + 2 + 5} \right)\\
 = \left( {x - 3} \right)\left( {x + 7} \right)\\
23){x^2} - 14x + 13\\
 = {x^2} - 14x + 49 - 36\\
 = {\left( {x - 7} \right)^2} - {6^2}\\
 = \left( {x - 7 - 6} \right)\left( {x - 7 + 6} \right)\\
 = \left( {x - 13} \right)\left( {x - 1} \right)\\
24)\\
{x^2} - 2x - 80\\
 = {x^2} - 2x + 1 - 81\\
 = {\left( {x - 1} \right)^2} - {9^2}\\
 = \left( {x - 1 - 9} \right)\left( {x - 1 + 9} \right)\\
 = \left( {x - 10} \right)\left( {x + 8} \right)\\
25){x^2} + 10x + 16\\
 = {x^2} + 10x + 25 - 9\\
 = {\left( {x + 5} \right)^2} - {3^2}\\
 = \left( {x + 8} \right)\left( {x + 2} \right)\\
26){x^2} - 12x + 11\\
 = {x^2} - 12x + 36 - 25\\
 = {\left( {x - 6} \right)^2} - {5^2}\\
 = \left( {x - 11} \right)\left( {x - 1} \right)\\
27)\\
{x^2} + 8x + 7\\
 = {x^2} + 8x + 16 - 9\\
 = {\left( {x + 4} \right)^2} - {3^2}\\
 = \left( {x + 7} \right)\left( {x + 1} \right)\\
28)4{x^2} - 4x - 3\\
 = 4{x^2} - 4x + 1 - 4\\
 = {\left( {2x - 1} \right)^2} - {2^2}\\
 = \left( {2x - 3} \right)\left( {2x + 1} \right)\\
29)\\
4{x^2} + 12x + 5\\
 = 4{x^2} + 12x + 9 - 4\\
 = {\left( {2x + 3} \right)^2} - {2^2}\\
 = \left( {2x + 5} \right)\left( {2x + 1} \right)\\
30)4{x^2} - 12x - 7\\
 = 4{x^2} - 12x + 9 - 16\\
 = {\left( {2x - 3} \right)^2} - {4^2}\\
 = \left( {2x - 7} \right)\left( {2x + 1} \right)
\end{array}$

21/ x^2+6x+5=(x^2+x)+(5x+5)=x(x+1) +5(x+1)=(x+5)(x+1)

22/ x^2+4x-21= (x^2 +7x) -(3x +21)=x(x+7)-3(x+7)=(x-3)(x+7)

23/ x^2-14x+13=(x^2-x) -(13x-13)=x(x-1)-13(x-1)=(x-1)(x-13)

24/ x^2 -2x+80=(x^2+8x)-(10x+80)=x(x+8)-10(x+8)=(x-10)(x+8)

25/ x^2 +10x+16x= (x^2+2x)+(8x+16)=x(x+2)+8(x+2)=(x+8)(x+2)

26/ x^2-12x+11= (x^2-x)-(11x-11)=x(x-1)-11(x-1)=(x-11)(x-1)

27/ x^2+8x+7=(x^2+x)+(7x+7)=x(x+1)+7(x+1)=(x+7)(x+1)

28/ 4x^2-4x-3=(2x)^2-2.2x+1-4=(2x-1)^2-2^2=(2x-1-2)(2x-1+2)=(2x-3)(2x+1)

29/ 4x^2+12x+5=(2x)^2+2.2x.3 +9-4=(2x+3)^2-2^2=(2x+3-2)(2x+3+2)=(2x+1)(2x+5)

30/ 4x^2-12x-7=(2x)^2-2.2x.3 +9 -16= (2x-3)^2-4^2=(2x-3-4)(2x-3+4)=(2x-7)(2x+1)